if p and q are the zeros of the quadratic polynomial 4x^2 - 1 = 0. find the value of p^2 + q^2...... pls ans in steps...... tiktok - anjela_g
Answers
Answer:
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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,
\begin{lgathered}\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} }}\end{lgathered}
p
2
+q
2
=(p+q)
2
−2pq
p
2
+q
2
=(0)
2
−2×(
4
−1
)
∴p
2
+q
2
=
2
1
Hence, the answer is ½.
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\large{\underline{\underline{\mathfrak{\heartsuit \: Extra \: Information: \: \heartsuit}}}}
♡ExtraInformation:♡
For a quadratic polynomial, ax² + bx + c, thr zeroes are α and β, where;
α + β = -b/a
αβ = c/a