Question

If kx2– 5x + 3 = 0 and 2x2 – kx + 1 = 0 have equal discriminants, then the value of k is :

(a) 1

(b) 2

(c)-2

(d) 3

Answer 1

Given :

Two quadratic equation as

k x² - 5 x + 3 = 0

2 x² - k x + 1 = 0

Both the equation have equal discriminant'

To Find :

The value of k

Solution :

Since, Discriminant = D =  b² - 4 a c

For the general quadratic equation a x² + b x + c = 0

Now,

Fore first quadratic equation , k x² - 5 x + 3 = 0

 $D_1$ = ( - 5 )² - 4 × k × 3

      = 25 - 12 k                 ..........1

Again

Fore second quadratic equation , 2 x² - k x + 1 = 0

 $D_2$ = ( - k )² - 4 × 2 × 1

      = k² - 8                        ..........2

According to question

Both The discriminant are equal

So, From eq 1 and eq 2

i.e      $D_1$ =   $D_2$

Or,   25 - 12 k =  k² - 8

Or,   k² - 8 - 25 + 12 k = 0

Or,   k² + 12 k - 33 = 0

Or,  K = $\dfrac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

         = $\dfrac{-12\pm \sqrt{(-12)^{2}-4\times 1\times (-33)}}{2\times 1}$

i.e k = 2.3 , -14.3

Hence, The value of k is 2 . Answer