Determine the quadratic equation whose solutions are 3 and −2. The best Maths tutors available 4.9 (36 reviews) 1st lesson free!  4.9 (30 reviews) 1st lesson free! 5 (16 reviews) 1st lesson free! 5 (32 reviews) 1st lesson free! 5 (16 reviews) 1st lesson free! 5 (22 reviews) 1st lesson free! 5 (17 reviews) 1st lesson free! 4.9 (8 reviews) 1st lesson free! 4.9 (36 reviews) 1st lesson free! 4.9 (30 reviews) 1st lesson free! 5 (16 reviews) 1st lesson free! 5 (32 reviews) 1st lesson free! 5 (16 reviews) 1st lesson free! 5 (22 reviews) 1st lesson free! 5 (17 reviews) 1st lesson free! 4.9 (8 reviews) 1st lesson free! Let's go Exercise 2Factor: Exercise 3Determine the value of k so that the two roots of the equation x² − kx + 36 = 0 are equal. Exercise 4The sum of two numbers is 5 and their product is −84. Find these numbers. Exercise 5Within 11 years, the age of Peter will be half the square of the age he was 13 years ago. Calculate the current age of Peter. Exercise 6To fence a rectangular farm of 750 m², 110 m of fence has been used. Calculate the dimensions of the farm. Exercise 7The three sides of a right-angled triangle are proportional to the numbers 3, 4 and 5. Find the length of each side knowing that the area of the triangle is 24 m². Exercise 8A rectangular garden 50 m long and 34 m wide is surrounded by a uniform dirt road. Find the width of the road if the total area of the garden and road is 540 m². Exercise 9Calculate the dimensions of a rectangle whose diagonal is 75 m, knowing that is similar to a rectangle with sides measuring 36 m 48 m respectively. Exercise 10Two natural numbers differ by two units and the sum of their squares is 580. What are these numbers? Exercise 11Two taps A and B fill a swimming pool together in two hours. Alone, it takes tap A three hours less than B to fill the same pool. How many hours does it take each tap to fill the pool separately? Exercise 12The length of the sides of a right-angled triangle are measured as three consecutive even numbers (in cm). Find the values of these sides. Exercise 13A rectangular piece of cardboard is 4 cm longer than wide. A box of 840 cm³ is constructed by using this piece of cardboard. A square of 6 cm is cut out in every corner and the rims are folded upwards to create the box. Find the dimensions of the box. Exercise 142 faucets can fill a tank in 1 hour and 20 minutes. The first faucet takes more than two hours longer to fill the same tank when functioning without the second tap. How long does it take to fill each one separately? Find the best Maths tutor on Superprof. Solution of exercise 1Determine the quadratic equation whose solutions are: 3 and −2. S = 3 − 2 = 1 P = 3 · 2 = 6 x² − x + 6 = 0 Solution of exercise 2Factor: Solution of exercise 3Determine the value of k so that the two roots of the equation x² − kx + 36 = 0 are equal. Find more learn Maths online here on Superprof. Solution of exercise 4The sum of two numbers is 5 and their product is −84. Find these numbers. Solution of exercise 5Within 11 years, the age of Peter will be half the square of the age he was 13 years ago. Calculate the current age of Peter. Current age x Age 13 years ago x − 13 Age within 11 years x + 11 Current age 21 Solution of exercise 6To fence a rectangular farm of 750 m², 110 m of fence has been used. Calculate the dimensions of the farm. Semiperimeter 55 Base x Height 55 − x x · (55 − x) = 750 x² − 55x + 750 = 0 x = 25 x = 30 The dimensions of the farm are 30 m and 25 m. Solution of exercise 7The three sides of a right-angled triangle are proportional to the numbers 3, 4 and 5. Find the length of each side knowing that the area of the triangle is 24 m². 1st side (base) 3x 2nd side (height) 4x 3rd side 5x 1st side 6 m 2nd side 8 m 3rd side 10 m Solution of exercise 8A rectangular garden 50 m long and 34 m wide is surrounded by a uniform dirt road. Find the width of the road if the total area of the garden and road is 540 m². (50 + 2x) · (34 + 2x) − 50 · 34 = 540 4x² + 168x − 540 = 0 x² + 42x − 135 = 0 x = 3 and x = −45 The road width is 3 m . Check for many great maths tutors in the UK here. Solution of exercise 9Calculate the dimensions of a rectangle whose diagonal is 75 m, knowing that it is similar to a rectangle with sides measuring 36 m 48 m respectively. Base 48x : 12 = 4x Height 36x : 12 = 3x (4x)² + (3x)² = 75² 25x² = 5625 x² = 225 x = 15 Base 4 · 15 = 60 m Height 3 · 15 = 45 m Solution of exercise 10Two natural numbers differ by two units and the sum of their squares is 580. What are these numbers? 1st number x 2nd number x + 2 1st number 16 2nd number 18 Solution of exercise 11Two taps A and B fill a swimming pool together in two hours. Alone, it takes tap A three hours less than B to fill the same pool. How many hours does it take each tap to fill the pool separately? Time of A x Time of B x + 3 A B A and B LCM(2, x, x + 3) = 2x (x + 3) Time of A 3 hours Time of B 6 hours Solution of exercise 12The length of the sides of a right-angled triangle are measured as three consecutive even numbers (in cm). Find the values of these sides. 1st leg 2x 2nd leg 2x + 2 Hypotenuse 2x + 4 (2x)² + (2x + 2)² = (2x + 4)² 4x² + 4x² + 8x + 4 = 4x² + 16x + 16 4x² − 8x − 12 = 0 x² − 2x − 3 = 0 x = 3 y x= −1 1st leg 6 cm 2nd leg 8 cm Hypotenuse 10 cm Solution of exercise 13A rectangular piece of cardboard is 4 cm longer than wide. A box of 840 cm³ is constructed by using this piece of cardboard. A square of 6 cm is cut out in every corner and the rims are folded upwards to create the box. Find the dimensions of the box. 6 (x − 12) · (x + 4 −12) = 840 (x − 12) · (x −8) = 140 x² − 20x − 44 = 0 x = 22 y x= −2 The dimensions are: 26 cm and 22 cm. Solution of exercise 142 faucets can fill a tank in 1 hour and 20 minutes. The first faucet takes more than two hours longer to fill the same tank when functioning without the second tap. How long does it take to fill each one separately? 1st Time x 2nd Time x − 2 1º 2º Between the two 1st Time 4 hours 2nd Time 2 hours What is the easiest way to solve quadratic word problems?Step I: Denote the unknown quantities by x, y etc. Step II: use the conditions of the problem to establish in unknown quantities. Step III: Use the equations to establish one quadratic equation in one unknown. Step IV: Solve this equation to obtain the value of the unknown in the set to which it belongs.
What is the quadratic formula answer?The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations.
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