Question

The value(s) of k for which the quadratic equation 3x2 - kx + 3 = 0 has
equal roots, is (are)

(A) 6

(B) -6

(C) + 6

(D) 9​

Answer 1

Answer:

k=+6 or -6

Step-by-step explanation:

we know that for equal roots

b²-4ac=0

k²-4*3*3=0

k²=36

k=+6 or -6

Answer 2

$\maltese$ Given :-

• The quadratic equation 3x² - kx +3 = 0 has equal roots

$\maltese$ To find:-

• Value of k

$\maltese$ SOLUTION :-

Since, the Quadratic equation has equal roots that means discriminant of the Quadratic equation is 0

Discriminant of the Quadratic equation is $b^2-4ac$

So,

Comparing with the general form of Quadratic equation ax²+bx+c  We get the values of a, b, c

$3x^2-kx+3=0$

$a=3$

$b = -k$

$c = 3$

$D=0$

$b^2-4ac =0$

$(-k)^2 - 4(3)(3) =0$

$k^2 -36=0$

$k^2 = 36$

$k = \pm\sqrt{36}$

$k = \pm \sqrt{(6)^2}$

$k = \pm 6$

So, the value of k is 6, -6

Correct option is - B,C

$\maltese$Know more about nature of roots:-

If a , b , c are real numbers

1) If D > 0 , then the roots are real and distinct.

2) If D = 0, then the roots are real and equal.

3) If D < 0 , then the roots are complex and conjugate to each other

If a , b , c are rational numbers

1) If D > 0 and 'D' is a perfect square then the roots are rational and distinct.

2) If D > 0 and 'D' not is a perfect square then the roots are irrational and conjugate to each other.

3) If D = 0 , then the roots are rational and equal.

4) If D < o , then the roots are not real and complex and conjugate to each other.