Question

write a quadratic polynomial sum of whose zeroes is-6 and pruduct of zeroes -4​

Answer 1

QUESTION:

write a quadratic polynomial sum of whose zeroes is-6 and pruduct of zeroes -4

ANSWER:

Quadratic equation is in the form of

$a {x}^{2} + bx + c = 0$

in other form;

b = sum of zeroes

c= product of zeroes.

suppose alpha and beta are the zeroes of the polynomial.

$a {x}^{2} - ( \alpha + \beta )x + \alpha \times \beta$

now come to main question;

$\alpha + \beta = - 6 \\ \\ \\ \\ \alpha \times \beta = - 4$

putting this value in the polynomial;

${x}^{2} - ( - 6)x + ( - 4)$

${x}^{2} + 6x - 4$

FINAL ANSWER;

$\huge\red{{x}^{2} + 6x - 4}$

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Answer 2

Given

• Sum of zeros = - 6
• Product of zeros = - 4

To Find

• Write the quadratic polynomial

Solution

★ Let the polynomial be ax² + bx + c

and its zeros be α and β

• Then, α + β = -6 = -b/a

And

• αβ = -4 = c/a

If a = 1, then b = 6 and c = -4

Hence, Quadratic polynomial is

x² + 6x - 4