Question

If ∝and β are the Zeros of the quadratic polynomialf(x)=x2-4x+3 find the value of 1/∝+1/β

Answer 1

Answer:

4/3

Step-by-step explanation:

p(x) = x^2 - 4x + 3

      = x^2 -x - 3x + 3

      = x(x - 1) -3(x - 1)

      = (x - 3)(x - 1)

Thus,

x = 3 or x = 1

α = 3 and β = 1

Now,

1/α + 1/β

1/3 + 1/1

(1+3)/3

4/3

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Answer 2

EXPLANATION.

α,β are the zeroes of the quadratic equation.

⇒ f(x) = x² - 4x + 3.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -(-4)/1 = 4.

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = 3/1 = 3.

To find :

⇒ 1/α + 1/β.

⇒ β + α/αβ.

Put the values in the equation, we get.

⇒ 4/3.

1/α + 1/β = 4/3.

                                                                                                                         

MORE INFORMATION.

Nature of the roots 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.