1.

If p and q are the zeros of the polynomial 4x^2-1=0 find the value of p^2+q^2

Answer»

Answer:

p² + q² = ½

Step-by-step EXPLANATION:

GIVEN polynomial :

4x² - 1 = 0, on comparing the given equation with ax² + bx + c = 0,

  • a = 4
  • b = 0
  • c = - 1

Sum of zeroes = -b/a

⇒ p + Q = 0/4

⇒ p + q = 0

Product of zeroes = c/a

⇒ pq = - 1/4

Now,

\sf p {}^{2} + q {}^{2} = (p + q) {}^{2} - 2pq \\ \\ \sf p {}^{2} + q {}^{2} =(0) {}^{2} - 2 \times ( \frac{ - 1}{4} ) \\ \\ \boxed{ \boxed{ \bf \therefore \: p {}^{2} + q {}^{2} = \frac{1}{2} }}

HENCE, the answer is ½.

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\large{\underline{\underline{\mathfrak{\heartsuit \: Extra \: Information: \: \heartsuit}}}}

For a quadratic polynomial, ax² + bx + c, thr zeroes are α and β, where;

  • α + β = -b/a
  • αβ = c/a


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