Question

What is the sum of the squares of the roots of the equation x2 + 2x - 143 = 0?

170
180
190
290

Answer 1

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 2

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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