Question

if the sum of the zeroes of the polynomial f(x) = 2x2 - 3kx - 5 is 6 , then the value of k is

Answer 1

EXPLANATION.

Sum of zeroes of the polynomial.

⇒ f(x) = 2x² - 3kx - 5 is 6.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -(-3k)/2 = 3k/2.

In question it is also given that,

Sum of zeroes = 6.

⇒ 3k/2 = 6.

⇒ 3k = 12.

⇒ k = 4.

                                                                                                                         

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, 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.

Answer 2

Given:-

• f(x) = 2x² - 3kx - 5

• Sum of Zeroes = 6

To Find:-

• Value of k

Solution:-

Comparing the given Equation with Standard equation i.e., ax² + bx + c = 0, we get

• a = 2

• b = -3k

• c = -5

Sum of the Zeroes = $\dfrac{-b}{a}$

$⟹6=\dfrac{-(-3k)}{2}$

$⟹6=\dfrac{3k}{2}$

$⟹k=\dfrac{6×2}{3}$

$⟹k=2×2$

${\boxed{⟹k=4}}$

Hence, The Value of K is 4.

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