write a quadratic equation with the following (no fractions or decimals)
Answers
Answer:
14. 8x²-26x+15 = 0
15. 48x²+70x+25 = 0
Step-by-step explanation:
14. given the roots are (3/4) and (5/2)
=> [x-(3/4)][x-(5/2)] are the factors
ie, (4x-3)(2x-5) are the factors
so, the product of factors = (4x-3)*(2x-5)
= 4x(2x-5) - 3(2x-5)
= 8x²-20x - 6x+15
= 8x²-26x+15
so, the quadratic equation is 8x² - 26x + 15 = 0
another method:
the quadratic equation given the root will be
x² - (sum of the roots)x + product of the roots = 0
here,
x² - ((3/4)+(5/2))x + (3/4)(5/2) = 0
x² - ((3/4)+(10/4))x + (15/8) = 0
x² - (13/4)x + (15/8) = 0
8x² - 8 (13/4)x +8 (15/8) = 0
8x² - 2 (13)x +15 = 0
8x² - 26x +15 = 0
14. given the zeroes are (-5/6) and (-5/8)
=> [x-(-5/6)][x-(-5/8)] are the factors
ie, (6x+5)(8x+5) are the factors
so, the product of factors = (6x+5)*(8x+5)
= 6x(8x+5) + 5(8x+5)
= 48x²+30x +40x+25
= 48x²+70x+25
so, the quadratic equation is 48x²+70x+25 = 0