Question

If m, n are the zeroes of the polynomial x² - 6 x + 6, then the value of m² + n² is​

Answer 1

Answer :

m² + n² = 24

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

Solution :

Here ,

The given quadratic polynomial is :

x² - 6x + 6

Now ,

Comparing the given quadratic polynomial with the general quadratic equation ax² + bx + c , we have :

a = 1

b = -6

c = 6

Also ,

It is given that , m and n are the zeros of the given quadratic polynomial .

Thus ,

• Sum of zeros = -b/a

→ m + n = -(-6)/1

→ m + n = 6

Also ,

• Product of zeros = c/a

→ mn = 6/1

→ mn = 6

Now ,

Using the identity

(A + B)² = A² + B² + 2AB ,

We have ;

=> (m + n)² = m² + n² + 2mn

=> 6² = m² + n² + 2×6

=> 36 = m² + n² + 12

=> m² + n² = 36 - 12

=> m² + n² = 24

Hence , m² + n² = 24