Question

find the value of z if the following equation has equal roots: (z-2)x2- (5+x)x + 16= 0

Answer 1

Answer:

= > ( z - 2 )x^2 + ( 5 + x )x + 16 = 0

= > zx^2 - 2x^2 + 5x + x^2 + 16 = 0

= > zx^2- 2x^2 + x^2 + 5x + 16 = 0

= > ( z - 1 )x^2 + 5x + 16 = 0

For any quadratic equation to have equal zeroes, discriminant must equal to 0.

discrminant, for ax^2 + bx + c = 0, is given by b^2 - 4ac.

Here,

b = 5

c = 16

a = z - 1

= > b^2 - 4ac = 0

= > 5^2 - 4(16)(z-1) = 0

= > 25 - 64(z-1) = 0

= > (25/64) + 1 = z

= > 89/64 = z

Hence the satisfying value of z is 89/64.