kx(x – 2) + 6 = 0

or kx^{2} – 2kx + 6 = 0

Comparing the given equation with ax^{2} + bx + c = 0, we get

a = k, b = – 2k and c = 6

We know, Discriminant = b^{2} – 4ac

= ( – 2k)^{2} – 4 (k) (6)

= 4k^{2} – 24k

For equal roots, we know,

b^{2} – 4ac = 0

4k^{2} – 24k = 0

4k (k – 6) = 0

Either 4k = 0 or k = 6 = 0

k = 0 or k = 6

However, if k = 0, then the equation will not have the terms ‘x^{2}‘ and ‘x‘.

Therefore, if this equation has two equal roots, k should be 6 only.

Answered by Pragya Singh | 1 year agoA natural number when increased by 12 equals 160 times its reciprocal. Find the number.

Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is \( \dfrac{29}{20}\) Find the original fraction.

The sum of the squares of two consecutive even numbers is 340. Find the numbers.

The sum of the squares of two consecutive multiple of 7 is 637. Find the multiples.