What is the sum of the squares of the roots of the equation x2 + 2x - 143 = 0?
170
180
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290
Answers
Answer:
Step-by-step explanation:
Let the roots be α and β. So, sum of squares of roots = α2 + β2
Sum of roots = α + β = -b/a = -2
Product of roots = αβ = c/a = -143
α2 + β2 = (α + β)2 - 2αβ
= (-2)2 - (-143) = 290
The correct option is D.
Answer:
Sum of the squares of the the roots = 290
Step-by-step explanation:
Given that,
x² + 2x - 143 = 0
Now,Comparing the above equation with the ax² + bx + c = 0,
We get,
a = 1, b = 2, c = - 143
Let the two roots are α and β.
∴Sum of the roots (α + β) = - (b/a)
⇒α + β = -2
and,
Product of the roots(α × β) = c/a
⇒ α × β = -143
∴Sum of the squares of the roots = α² + β²
= (α + β)² - 2αβ
= (-2)² - 2×(- 143)
= 4 + 286
= 290
∴Sum of the squares of the root of the equation = 290
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