24. If a and ß zeros of p(x) =x2+x-1,
then value of 1/a + 1/B =
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EXPLANATION.
α and β are the zeroes of the polynomial.
⇒ p(x) = x² + x - 1.
As we know that,
Sum of the zeroes of the quadratic equation.
⇒ α + β = -b/a.
⇒ α + β = -(1/1) = -1.
Products of the zeroes of the quadratic equation.
⇒ αβ = c/a.
⇒ αβ = -1.
To find :
⇒ 1/α + 1/β.
⇒ β + α/αβ.
Put the values in the equation, we get.
⇒ (-1)/(-1) = 1.
⇒ 1/α + 1/β = 1.
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.
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