Question

please answer this!!​

Answer 1

Given:

F(x) = x² + 2(k+2)x +9k = 0

has equal roots .

To find :

• The value of K .

Solution :

• As we know that , for equal roots discriminant of the equation must be zero,

• D = b²-4ac =0

Here ,

• a= 1 , b = 2(k+2) and c = 9k

=> b²-4ac=0

=> (2(k+2))²-4(1)(9k)=0

=> 4(k+2)²-4(9k)=0

=> (k+2)²-9k=0

=> k²+4+4k-9k=0

=> k²-5k+4=0

=> k² -4k-k+4=0

=> k(k-4)-1(k-4)=0

=> (k-1)(k-4)=0

=> k = 1 , 4

Hence , option a is correct

Answer 2

Question:-

If the equation x² + 2(k + 2)x + 9k = 0 has equal roots then k = ?

Answer:-

We know that if an equation has equal roots, then it's discriminant (D) must be equal to 0

→ D = b² - 4ac

Given Quadratic Equation:- x² + 2(k + 2)x + 9k = 0

Here,

• a = 1
• b = 2(k + 2)
• c = 9k

So,

D = 0

→ b² - 4ac = 0

→ b² = 4ac

→ [2(k + 2)]² = 4 * 1 * 9k

→ 2² * [ k² + 2² + 2(k)(2) ] = 4 * 9k

→ k² + 4 + 4k = 9k

→ k² - 5k + 4 = 0

→ k² - 4k - k + 4 = 0

→ k(k - 4) - 1(k - 4) = 0

→ (k - 4)(k - 1) = 0

Hence,

Either, (k - 4) = 0

→ k = 4

Or, (k - 1) = 0

→ k = 1

So, k = 1 or 4

Ans. Option (a) => 1 or 4