Question

if a and ß are zeroes of x² - 4x + 1,
find the value of 1/a+1/ß-aß​

Answer 1

Answer:

Given: α,β are zeroes of the polynomial x2−4x+1

To find the value of α1+β1−αβ

Sol: From the given quadratic equation,

α+β=4 and αβ=1

Therefore, 

α1+β1−αβ=αβα+β−αβ⟹=4−1=3

Answer 2

EXPLANATION.

α,β are the zeroes of the polynomial,

⇒ F(x) = x² - 4x + 1.

As we know that,

Sum of zeroes of a quadratic equation,

⇒ α + β = -b/a.

⇒ α + β = -(-4)/1 = 4.

Products of zeroes of quadratic equation,

⇒ αβ = c/a.

⇒ αβ = 1/1 = 1.

To find value of,

⇒ 1/α + 1/β - αβ.

⇒ β + α - (αβ)²/αβ.

Put the values in the equation, we get.

⇒ 4 - (1)²/1.

⇒ 4 - 1.

⇒ 3.

                                                                                                                 

MORE INFORMATION.

Nature of the factors of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.