Question

Findthe value of k so that ithas two real and equal roots k+4x2+k+x+1

Answer 1

Correct question: Find the value of k so that it has two real and equal roots (k + 4x²) + (k + x) + 1

GIVEN :

(k + 4x²) + (k + x) + 1

We know that when there are two equal and real roots then,

Discriminant = 0

Discriminant formula = b² - 4ac

0 = (k + 1)² - 4(k + 4)(1)

0 = k² + 2(k)(1) + 1² - 4k - 16

0 = k² + 2k + 1 - 4k - 16

0 = k² - 2k - 15

Split the middle term

k² - 2k - 15 = 0

k² - 5k + 3k - 15 = 0

k(k - 5) + 3(k - 5) = 0

k + 3 = 0 or k - 5 = 0

k = -3 or k = 5

Therefore, the value of k is -3 or 5

Answer 2

QUESTIONS -

Find the value of k so that it has two real and equal roots (k + 4x²) + (k + x) + 1

$\bf\huge\boxed{ANSWERS}$

Equations : (k + 4x²) + (k + x) + 1

Quadratic equation states that when the two equal root exist then their discriminant must be equal to zero

$\bf\huge\boxed{D=0}$

Formula of D = b² - 4ac

0 = (k + 1)² - 4(k + 4)(1)

0 = k² + 2(k)(1) + 1² - 4k - 16

0 = k² + 2k + 1 - 4k - 16

0 = k² - 2k - 15

By splitting middle term

k² - 2k - 15 = 0

k² - 5k + 3k - 15 = 0

k(k - 5) + 3(k - 5) = 0

k + 3 = 0 | k - 5 = 0

k = -3 or k = 5

Hence the value of k are - 3 & 5

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