Question

Find
95. Determine k such that the quadratic equation k(x - 2)x+ 6 = 0 has equal roots-​

Answer 1

EXPLANATION.

Quadratic equation,

⇒ k(x - 2)x + 6 = 0.

quadratic equation has equal roots,

As we know that,

D = Discriminant = b² - 4ac.

⇒ k(x - 2)x + 6 = 0.

⇒ k(x² - 2x) + 6 = 0.

⇒ kx² - 2kx + 6 = 0.

⇒ (-2k)² - 4(k)(6) = 0.

⇒ 4k² - 24k = 0.

⇒ k(4k - 24) = 0.

⇒ k = 0  Or  k = 6.

                                                                                                                     

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

Answer:

Value of k=6

Step-by-step explanation:

Given Quadratic equation:-

kx²-2kx+6=0 has equal roots.

Compare above equation with

ax²+bx+c=0 we get

a = k , b = -2k , c = 6

Now ,

Discreminant (D)=0

/* given roots are equal */

b²-4ac=0

⇒(-2k)²-4×(k)×6 = 0

⇒4k²-24k=0

⇒4k(k-6)=0

⇒4k=0 Or k-6=0

⇒k=0 Or k=6

Here , k = 0 is not possible.

Therefore,.

Value of k=6

Learn more!!!

(i). If b² - 4ac > 0, the quadratic equation has two distinct real roots.

(ii). If b² - 4ac = 0,  the quadratic equation has two equal real roots.

(iii). If b² - 4ac < 0, the quadratic equation has no real roots.

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$Hope \: it \: helps!$