Question

If the product of zeroes of the polynomial, f(x) = ax² + 3x +7 is -7, then a is ______________.

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Answer 1

$\bf{\Huge{\underline{\boxed{\sf{\red{ANSWER\::}}}}}}$

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

If the product of zeroes of the polynomial, f(x) = ax² + 3x + 7 is -7.

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

The value of a.

$\bf{\Large{\boxed{\sf{\pink{Explanation\::}}}}}$

Let f(x) = ax² + 3x + 7

We have,

$\sf{Product\:of\:zeroes\:=\:-7}$

This compared by Ax² + Bx + C, so;

• A = 1
• B = 3
• C = 7

We know that,

• $\bf{\large{\boxed{\sf{\orange{Product\:of\:zeroes\::}}}}}$

$\leadsto\sf{\alpha \beta \:=\:\frac{c}{a} }$

Therefore,

$\longmapsto\sf{-7\:=\:\frac{7}{a} }$

$\longmapsto\sf{\:-7a=7}$

$\longmapsto\sf{a\:=\cancel{\frac{-7}{7} }}$

$\longmapsto\sf{\red{a\:=\:-1}}$

Thus,

$\bf{\Large{\boxed{\sf{\pink{The\:value\;of\:a\:is\:-1}}}}}$

Answer 2

Answer:

$\large\boxed{\sf{a=-1}}$

Step-by-step explanation:

Given a quadratic function such that,

$\sf{f(x) = a {x}^{2} + 3x + 7}$

Let's head to the general form of quadratic function.

The general form is given by expression,

• $\large \boxed{ \sf{A{x}^{2} + Bx + C}}$

Comparing the Coefficient, We have,

• A = a
• B = 3
• C = 7

We know that, Product of roots is given by $\sf{\dfrac{C}{A}}$

But, It's given that Product of roots is -7

Therefore, We have,

$\sf{ = > \frac{C}{A} = - 7} \\ \\ \sf{ = > \frac{ 7}{a} = - 7 }\\ \\ \sf{= > a = \frac{ 7}{ - 7} }\\ \\ \sf{= > a = -1}$