Question

2
8. If p and q are the zeroes of the quadratic polynomial x^2 + mx + n^2. Then find the value of
p^2 + pq+q^2.​

Answer 1

Answer:

p²+pq+q² = m² - n²

Step-by-step explanation:

If p and q are the zeroes of the quadratic polynomial x² + mx + n² = 0, then p+q = -m and pq = n²

Also, p²+pq+q² = p²+2pq+q² - pq = (p+q)² - pq = (-m)² - n² = m² - n²

Answer 2

Answer:

m² - n²

Note:

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

★ To find the zeros of the polynomial p(x) , operate on p(x) = 0 .

★ A quadratic polynomial can have atmost two zeros .

★ 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

★ If α and ß are the zeros of any quadratic polynomial , then it is given by ;

x² - (α + ß)x + αß

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then they (α and ß) are also the zeros of the quadratic polynomial k(ax² + bx + c) , k≠0.

Solution:

Hence,

The given quadratic polynomial is ;

x² + mx + n²

Also,

It is given by that p and q are the zeros of the given quadratic polynomial .

Thus,

Sum of zeros will be ;

p + q = -m/1 = -m

Also,

Product of zeros will be ;

pq = n²/ 1 = n²

Now,

p² + q² + pq = p² + q² + 2pq - pq

= (p² + q² + 2pq) - pq

= (p + q)² - pq

= (-m)² - n²

= m² - n²

Hence,

The required answer is :

m² - n²