Question

Write the quadratic polynomial whose sum of zero is 3 and product is 8​

Answer 1

${\underline{\underline{\bf{Given:}}}}$

• Sum of the Zeroes = 3
• Product of the Zeroes = 8

${\underline{\underline{\bf{To \: \: find :}}}}$

• Quadratic Polynomial

${\underline{\underline{\bf{Solution:}}}}$

✯ We know that Quadratic Polynomial is in the form of

• ax² + bx + c

✯ Sum of the Zeroes is

${ \boxed {\sf{Sum \: of \: the \: Zeroes = \alpha + \beta = \frac{ -b}{a} = \frac{ Coefficient \: of \: x }{Coefficient \: of \: x^{2}}}}}$

${\sf{Sum \: of \: the \: Zeroes = \cfrac{ -b}{a} }}$

${\sf{Sum \: of \: the \: Zeroes = - \cfrac{3 }{1} }}$

✯ Product of the Zeroes is

${ \boxed {\sf{Product \: of \: the \: Zeroes = \alpha \beta = \frac{ c}{a} = \frac{ Constant \: term}{Coefficient \: of \: x^{2}}}}}$

${\sf{Product \: of \: the \: Zeroes = \cfrac{ c}{a} }}$

${\sf{Product \: of \: the \: Zeroes = \cfrac{ 8}{1} }}$

✯ Form this we get

• a = 1
• b = -3
• c = 8

✯ Substituting the value of a, b and c in Quadratic Polynomial from :-

${ \large{ \bf{ \longmapsto{ax^{2} + bx + c }}}}$

${ \large{ \bf{ \longmapsto{(1)x^{2} + (-3)x + 8 }}}}$

${ \large{ \underline{ \boxed{ \bf{ \longmapsto{x^{2} -3x + 8 }}}}}}$

So, Quadratic Polynomial is x² - 3x + 8.