Question

Find a quadratic polynomial, the sum and the product of whose zeros are 3 and minus 4 by 5

Answer 1

Zeros are 3 and $\frac{-4}{5}$

___________ [GIVEN]

• We have to form a quadratic equation.

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• Let $\alpha$ = 3

• $\beta$ = $\dfrac{-4}{5}$

Now..

Sum of zeros = $\alpha$ + $\beta$

=> 3 + $\dfrac{(-4)}{5}$

=> $\dfrac{15\:-\:4}{5}$

=> $\dfrac{11}{5}$ _______ (eq 1)

Product of zeros = $\alpha$$\beta$

=> 3 × $\dfrac{(-4)}{5}$

=> $\dfrac{-12}{5}$ _______ (eq 2)

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We know that..

x² - (Sum of zeros)x + Product of zeros = 0

=> x² - $(\dfrac{11}{5})$x + $\dfrac{(-12)}{5}$ = 0

=> $\dfrac{5 {x}^{2} \: - \: 11x \: - \: 12}{5}$ = 0

=> 5x² - 11x - 12

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5x² - 11x - 12 is the quadratic equation whose zeros are 3 and $\frac{-4}{5}$.

________ [ANSWER]

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