Question

find the value of k , if the roots of the following equation:
x^2 -6x+( k+7 ) =0 ( quadratic equation )​

Answer 1

Required Answer :

• The value of k = 16

Given :

• The roots of the following equation are equal :
• x² - 6x + (k + 7) = 0

To find :

• The value of k = ?

Solution :

Here, we are given that the roots of the equation = x² + 6x + (k + 7) = 0 are equal and we need to calculate the value of k. So, for that we will use the discriminant formula.

• D = b² - 4ac

⇒ x² + 6x + (k + 7) = 0

Comparing with ax² + bx + c = 0

we have,

• a = 1
• b = 6
• c = (k + 7)

⇒ (6)² - 4(1)(k + 7) = 0

⇒ (6 × 6) - 4(k + 7) = 0

⇒ 36 - 4k + 28 = 0

⇒ 64 - 4k = 0

⇒ - 4k = - 64

⇒ Cancelling the (-) sign :

⇒ 4k = 64

⇒ k = 64/4

⇒ Cancelling by 2 :

⇒ k = 32/2

⇒ Cancelling by 2 :

⇒ k = 16

Therefore, the value of k = 16

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Know More :

⇒ When b² - 4ac = 0

• The roots are equal.

⇒ When b² - 4ac > 0

• The roots are real and unequal.

⇒ When b² - 4ac < 0

• The roots are imaginary.