Question

if p and q are the zero of quadratic polynomial x^2+mx +n^2+ a then value of p^2 +q^2+pq is​

Answer 1

Answer:

Step-by-step explanation:

0

Answer 2

Answer:

m² - n² - a

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 + a)

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 + a) / 1 = n² + a

Now,

p² + q² + pq = p² + q² + 2pq - pq

= (p² + q² + 2pq) - pq

= (p + q)² - pq

= (-m)² - (n² + a)

= m² - n² - a

Hence,

The required answer is :

m² - n² - a