Question

If a and ß are the zeros of polynomial P(x) = ax2 + bx+c. Find the value of 1/α + 1/β​

Answer 1

EXPLANATION.

α and β are the zeroes of the polynomial.

⇒ p(x) = ax² + bx + c.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

To find : 1/α + 1/β.

⇒ 1/α + 1/β.

⇒ (β + α)/(αβ).

Put the values in the equation, we get.

⇒ (-b/a)/(c/a).

⇒ (-b/a) x (a/c) = (-b/c).

⇒ 1/α + 1/β = (-b/c).

                                                                                                                     

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

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