Question

find the quadratic polynomial where sum and product of the zeroes -8/3 and 4/3 respectively​

Answer 1

Answer:

$\tt \: x²- \frac{8}{3}x+ \frac{4}{3}$

$\sf\small{ \underline{\underline\red{ \pmb{ Note:-}}}}$

☆The possible values of the variable for which the polynomial becomes zero are called its zeros.

☆A quadratic polynomial can have atmost two zeros.

☆The general form of a quadratic polynomial is given as ; ax² + bx + c.

☆If a and are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros, (a + B) = -b/a

★Product of zeros, (a) = c/a

If a and are the zeros of a quadratic polynomial, then that quadratic polynomial is given as: k.[x² - (a + B)x+ aB ], k * 0.

$\sf\small{ \underline{\underline\red{ \pmb{ Solution:-}}}}$

• Given Sum of zeros, (a + B) = -8/3 Product of zeros, (a) = 4/3

• To find : A quadratic polynomial

We know that, If a and I are the zeros of a quadratic

polynomial, then that quadratic polynomial is given as: k.[x² - (a + B)x+ aß], k0.

Thus,

Required quadratic polynomial will be given as:

$\tt \implies \: k[x² - (a +ß )x+ aß], k = 0 \\ \\ \tt \implies \: k[ x² - \frac{ - 8}{3} x + \frac{4}{3} ] \\ \\ \tt \implies \: k = 0$

If k = 1, then the quadratic polynomial will be: x² - 8/3x + 4/3.

Hence, Required quadratic polynomial is :

$\tt \: x² - \frac{8}{3} x + \frac{4}{3}$