Question

If p,q are 0s of polynomial f(x)=2x²-7x+3 find the value of p²+q²

Answer 1

Answer:-

Given Polynomial => 2x² - 7x + 3

Let , a = 2 ; b = - 7 and c = 3

We know that,

Sum of the roots = - b/a

→ p + q = -(-7/2)

→ p + q = 7/2 -- equation (1)

Product of the roots = c/a

→ pq = 3/2 -- equation (2)

We know,

(a + b)² = a² + b² + 2ab

→ a² + b² = (a + b)² - 2ab

→ p² + q² = (p + q)² - 2ab

Putting the values from equation (1) & (2) we get,

→ p² + q² = (7/2)² - 2(3/2)

→ p² + q² = 49/4 - 6/2

Taking LCM in RHS we get,

→ p² + q² = (49 - 12)/4

→ p² + q² = 37/4

Hence, the value of p² + q² is 37/4.

Answer 2

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