Question

Searches related to if ax^2+9x+15 is a quartic polynomial and product of its zeroes is -6 , then find teh value of a

Answer 1

Answer :

The value of a is -5/2

Given :

The quadratic polynomial is :

• ax² + 9x + 15
• The product of zeroes is -6

To Find :

• The value of a

Concept to be Used :

★ Relationship between the zeroes and the coefficients of the polynomial :

$\sf{Sum \: \: of \: \: the \: \: zeroes = -\dfrac{coefficient \: \: of \: \: x}{coefficient \: \: of \: \:x^{2}}}$

$\sf{Product\: \: of \: \: the \: \: zeroes = \dfrac{constant \: \: term}{coefficient \: \: of \: \:x^{2}}}$

Solution :

Using the relation of product of zeroes in given polynomial :

$\sf \implies - 6 = \dfrac{constant \: \: term}{coefficient \: \: of \: x {}^{2} } \\ \\ \sf \implies - 6 = \dfrac{15}{a} \\ \\ \sf \implies a = \frac{15}{ - 6} \\ \\ \implies \bf a = - \frac{5}{2}$

Answer 2

Answer:

The product of zeroes in the given polynomial:

$- 6 \times \frac{the \: constantterm}{coefficient \: of \: {x}^{2} \: }$

$- 6 \times \frac{15}{a}$

$a = \frac{15}{ - 6}$

$a = - \frac{5}{2}$