Question

4) find the value of k, if one of the roots of the
quadratic equation : kx2-11x-6=0 is -1/2​

Answer 1

EXPLANATION.

One roots of the quadratic equation.

⇒ kx² - 11x - 6 = 0  is  -1/2.

As we know that,

Put the value of x = -1/2 in equation, we get.

⇒ k(-1/2)² - 11(-1/2) - 6 = 0.

⇒ k(1/4) + 11/2 - 6 = 0.

⇒ k/4 + 11/2 - 6 = 0.

⇒ k + 22 - 24 = 0.

⇒ k - 2 = 0.

⇒ k = 2.

                                                                                                                                               

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.

Answer 2

Required Answer:

★ The value of k is 2 if one of the root of the roots of the quadratic equation is kx² - 11x - 6 = 0 is -1/2

Step-by-step explanation:

To solve this question procedure is given below: To solve this question we just have to put -1/2 at the place of x. Why we have to put that there at the place of x it is because of a simple reason that we have to find the value of k. Let us solve this question!

⟹ kx² - 11x - 6 = 0

⟹ k(-1/2)² - 11(-1/2) - 6 = 0

⟹ k(-1/2)(-1/2) - 11(-1/2) - 6 = 0

⟹ k(1/2)(1/2) - 11(-1/2) - 6 = 0

⟹ k(1/4) - 11(-1/2) - 6 = 0

Rule: (- × - be + always!)

⟹ k(1/4) +11/2 - 5 = 0

⟹ ${\sf{\dfrac{(1 \times k) + (2 \times 11) - (4 \times 5)}{4}}}$

⟹ ${\sf{\dfrac{k + 22 - 20}{4}}}$

⟹ ${\sf{\dfrac{k + 22 - 20}{4}}}$

⟹ ${\sf{\dfrac{k + 2}{4}}}$

⟹ k = 4/2

⟹ k = 2

Henceforth, the value of k is 2.

Additional information:

Knowledge about Quadratic equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation

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