Question

quadratic polynomial having zeros as 4 and -6

Answer 1

${x}^{2} + 2x - 24 = 0$

Answer 2

Answer:

$x^2 + 2x - 24 = 0$ is the required quadratic polynomial.

Step-by-step explanation:

Explanation:

Given that, 4 and -6 are the zeroes of the quadratic polynomial.

In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.

As we know, quadratic polynomial with  $\alpha \ and \ \beta$  as zeroes can be written as,

$x^2 - (\alpha + \beta )x + \alpha \beta$

So, $\alpha$ = 4 and $\beta$ = -6.

Step 1:

We have, 4 and -6 are the zeroes of the quadratic polynomial.

So, $\alpha + \beta$ = (4 -6) = -2

and $\alpha \beta$ = 4 × -6 = -24

Now, the quadratic polynomial is,

⇒ $x^2 - (\alpha + \beta )x + \alpha \beta$

⇒$x^2 - (-2)x + -24$

⇒ $x^2 + 2x - 24 = 0$

Final answer:

Hence, $x^2 + 2x - 24 = 0$ is the required quadratic polynomial.

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