Question

for what value of k does the quadratic equation 4 x square - 12 x - k = 0 have no real roots

Answer 1

Answer:

Step-by-step explanation:

b2-4ac

(-12)2-4(4)(-k)

144+16k

16k= -144

K= -144/16

K=-9

Answer 2

Answer:

• ★ Therefore , k < - 9 the Quadratic equation will have no real roots

Step-by-step explanation:

★ Given :

• 4 x ² - 12 - k = 0

★ We know that :

To have no real roots the discriminate should be less than zero

D = b ² - 4 ac

b² - 4 ac < 0

★ Solution :

: $\implies$ Given equation is 4 x ² - 12 x - k = 0

: $\implies$ For equation to have no real roots

: $\implies$ D < 0 or b² - 4 ac < 0

: $\implies$ a = 4 b = -12 C = - K

: $\implies$ ( - 12 ) ² - 4 × 4 × ( - K ) < 0

: $\implies$ 144 + 16 k < 0

: $\implies$ 16 k < - 143

: $\implies$ K < - 9

Therefore , k < - 9 the Quadratic equation will have no real roots

Know more :

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• The equation of the form ax² + bx + c = 0, where a, b, c are real numbers and a0 is called a quadratic equation.

• The value of unknown variable x, which satisfies the given quadratic equation is called the roots of quadratic equation. For example, if is a root of quadratic equation ax2 + bx + c = 0, then a2 + b + c = 0.

• The quadratic formula for finding the roots of quadratic equation ax2 + bx + c = 0 is given by x = [-b ± √(b2 - 4ac)]/2a.

• It helps us to find the roots of a quadratic equation very easily by replacing the other methods of finding the roots like, factorisation method, completing the square method.

• The quadratic formula can be used for both factorable and non-factorable quadratic equations to find their roots in a simple manner.

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