Math, asked by pdayan084, 2 months ago

write a quadratic equation with the following (no fractions or decimals)


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Answers

Answered by ravi2303kumar
1

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

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