Question

Or
Find the quadratic polynomial, sum of whose zeroes is 2 and product is - 8. Hence find the zeroes
of the polynomial.
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Answer 1

Answer:

Question -:

$\bigstar$ Find the quadratic polynomial, sum of whose zeroes is 2 and product is - 8. Hence find the zeroes of the polynomial.

《☆》 Given -:

• Sum Of Zeroes = 2.
• Product of zeroes = -8.

《☆》 To Find -:

• Quadratic polynomial.
• Zeroes of the Polynomial.

《☆》 Solution -:

Let,

The zeroes of the polynomial be $\alpha\ and\ \beta$.

Therefore,

• Sum of Zeroes $[ \alpha + \beta ]$ = 2.
• Product of zeroes $[ \alpha × \beta ]$ = -8.

So,

We can get the Quadratic polynomial by the formula,

$X^2-[ \alpha + \beta ]X +[ \alpha × \beta ]$

By putting the values, we get,

• $X^2-[2 ]X +[ -8]$
• $X^2-2X-8$

Now, for finding the values of the zeroes $[ \alpha\ and\ \beta ]$

We will use the method - Splitting of the middle term

$X^2-2X-8=0 \\ X^2-[4-2]X-8=0 \\X^2-4X+2X-8=0 \\X[X-4]+2[X-4]=0 \\ [X-4][X+2]=0 \\ \boxed {X=4,-2}$

《☆》Answer -:

• Quadratic polynomial = $X^2-2X-8$.
• Zeroes of the Polynomial = X = 4, -2.