Question

If x=2 is a root of the polynomial f(x)=2x2-3x+7a.find a x=2. find a​

Answer 1

Answer:-

The Required Value of 'a' is -2/7.

Explanation:-

Given:-

• A polynomial f(x) = 2x² - 3x + 7a.

• x = 2 is the root of the given polynomial.

To Find:-

• The value of x.

What is a root of a polynomial??

• A root of the polynomial is the value of variables in the polynomial for which the result would be equal to zero.

• Let a polynomial ax² + bx² + c, it would be equal to zero if x = Root of the polynomial, and a, b and c are constant terms.

Now,

Since here the root of the polynomial is given as 2,

↦ 2x² - 3x + 7a = 0, where x = 2.

↦ 2(2)² - 3(2) + 7a = 0.

(By putting the root of the f(x) I.e. x = 2).

↦ 2(4) - 6 + 7a = 0.

↦ 8 - 6 + 7a = 0.

↦ 2 + 7a = 0.

↦ 7a = -2.

↦ a = -2/7.

Therefore The Required Value of a is -2/7.