Question

write a quadratic polynomial whose zeroes are prime factor if 6​

Answer 1

Amswer:-

The Required Quadratic Polynomial Is, $\tt\bf x^2-5x+6.$

Explanation:-

Given:-

• Zeroes of a qaudratic polynomial are prime factors of 6.

To Find:-

• The quadratic polynomial.

Concept Used:-

• A quadratic polynomial is always in the form of $\bf x^2-(a+b)x+ab,$ where a, and b are zeroes of the polynomial.

Solution:-

We have given the zeroes of the polynomial (i.e. a and b) are prime factors of 6,

We can write 6 as 2×3

So indirectly the question had given us 2 and 3 as the zeroes of the polynomial (say a = 2 and b = 3).

So,

$\\ \bf\gg a + b = 2 + 3 = 5\:\: ----eq(1)$

And,

$\\ \bf\gg a\times b = 2\times 3 = 6\:\: ----eq(2)$

Therefore The Required Quadratic Equation is:-

$\\ \tt\mapsto x^2-(a+b)x+ab.$

$\\ \bf = x^2-5x+6.$

$\\ \rm\bigg(from\ eq(1)\ and\ eq(2)\bigg).$