Question

find the value of c for which the quadratic equation
4x² - 2 (c + 1) x + (c + 4) = 0 has
quadrati e cquation
equal roots.​

Answer 1

Answer:

Value of c = 5 Or c = -3

Step-by-step explanation:

Compare given Quadratic equation 4x²-2(c+1)x+(c+4)=0 with Ax²+Bx+C = 0, we get

A = 4, B = -2(c+1), C = (c+4)

Discreminant (D) = 0

/* Given roots are equal */

B²-4AC = 0

=> [-2(c+1)]² - 4×4×(c+4)=0

=> 4(c+1)² - 16(c+4)=0

/* Divide each term by 4, we get

=> (c+1)² - 4(c+4)=0

=> c²+2c+1-4c-16=0

=> c²-2c-15=0

/* Splitting the middle term, we get

=> c²-5c+3c-15=0

=> c(c-5)+3(c-5)=0

=> (c-5)(c+3)=0

=> c-5 = 0 Or c+3 = 0

=> c = 5 Or c = -3

Therefore,

Value of c = 5 Or c = -3

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