Question

find all quadratic polynomial whose product and sum of zeros are minus 1 by 3 and minus 7 by 2 respectively​

Answer 1

Answer:

Required Polynomial is 6x² + 21x - 2.

Step-by-step explanation:

Given:

• Sum of Zeroes = -7/2
• Product of Zeroes = -⅓

We have:

• General Formula of Quadratic Polynomial:

→ f(x) = x² - (a + b)x + ab

Substitute obtained value in Formula:

• x² - ( -7/2)x + (-⅓)

→ x² + 7/2x - 1/3

→ 6x² + 21x -2 = 0

• Therefore, The Required Polynomial is 6x² + 21x - 2.

Answer 2

Quadratic Polynomials :

Given, Product of zeroes = $\mathsf{\dfrac{-1}{3}}$

Sum of the zeroes = $\mathsf{\dfrac{-7}{2}}$

By using General Quadratic Equation,

$\boxed{\mathsf{{x}^{2}\:-\:( \:Sum \:of\:zeroes\:)x \:+\:Product\:of\:zeroes}\:=\:0}$

$\mathsf{{x} ^{2}\:+\:{\dfrac{7x}{2}\:-\:{\dfrac{1}{3}\:=\:0}}}$

Taking L. C. M.,

⛛ $\mathsf{{6x} ^{2}\:+\:21x\:-\:2\:=\:0}$