Question

Find the quadratic polynomial, the sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.

Answer 1

Answer:

• Quadratic polynomial = x² - 8x + 16
• Zeroes = 6 and 2

Step-by-step explanation:

Given that:

• The sum of the zeroes of the quadratic polynomial is 8.
• The product of the zeroes of the quadratic polynomial is 12.

To find :

• The quadratic polynomial.
• The zeroes of the quadratic polynomial.

Solution :

Let the zeroes of the quadratic polynomial be α and β respectively.

According to the question,

Sum of zeroes = 8

⇒ α + β = 8

And, product of zeroes = 12.

⇒ αβ = 12

We know that,

The quadratic polynomial is written as,

= x² - (α + β)x + αβ

= x² - 8x + 12

Hence, the required quadratic polynomial is x² - 8x + 12.

Now, to find the zeroes of the quadratic polynomial ;

$\implies \sf {x}^{2} - 8x + 12 = 0 \\ \\ \implies \sf {x}^{2} - 6x - 2x + 12 = 0 \\ \\ \implies \sf x(x - 6) - 2(x - 6) = 0 \\ \\ \implies \sf (x - 6)(x - 2) = 0 \\ \\ \implies \sf x = 6 \: \: or \: \: x = 2$

Hence, the zeroes of the quadratic polynomial are 6 and 2.

Answer 2

Answer:

.

=k(x²-(α+β)x+αβ)

=k(x²-8x+12)

here k=1

=x²-8x+12

=x²-2x-6x+12

=x(x-2)-6(x-2)

=(x-2)(x-6)

⇒x-2=0 or ⇒x-6=0

⇒x=2 or ⇒x=6