Find the value of k for quadratic equation kx^2+(2k+4)x+9=0,so that they have two equal roots
Answers
Answer:
A quadratic equation is said to have equal roots if its discriminant is equal to zero.
Discriminant is a equation which is calculated based on the coefficients of the terms in a quadratic equation. There are three cases to define nature of roots for a given quadratic equation.
- D > 0
- D = 0
- D < 0
D is the discriminant which is written as: b² - 4ac
Here,
- 'a' is the coefficient of x²
- 'b' is the coefficient of x
- 'c' is the constant term
E.g. : x² - 5x + 6
Here, a = 1 ; b = 5 ; c = 6
Coming to your question,
Given quadratic equation: kx² + ( 2k + 4 ) x + 9 = 0
From this we get,
- a = k
- b = 2k + 4
- c = 9
Substituting them in the equation of discriminant we get,
→ ( 2k + 4 )² - 4 ( k ) ( 9 )
→ 4k² + 16k + 16 - 36k
→ 4k² - 20k + 16
Since the question says the equation has equal roots, we equate the above D to zero. Hence we get,
→ 4k² - 20k + 16 = 0
→ 4k² - 4k - 16k + 16 = 0
→ 4k ( k - 1 ) - 16 ( k - 1 ) = 0
→ ( 4k - 16 ) ( k - 1 ) = 0
→ k = 4, 1
Therefore the given equation can have 'k' value as 1 as well as 4.
Answer:
k = 4 or k = 1 .
Step-by-step explanation:
Given :
P ( x ) = k x² + ( 2 k + 4 ) x + 9
We know :
For equal root D = 0
i.e. b² - 4 a c = 0
( 2 k + 4 )² - 4 × k × 9 = 0
4 k² + 16 + 16 k - 36 k = 0
4 k² - 20 k + 16 = 0
k² - 5 k + 4 = 0
k² - 4 k - k + 4 = 0
k ( k - 4 ) - ( k - 4 ) = 0
( k - 4 ) ( k - 1 ) = 0
k = 4 or k = 1 .
Hence , the value of k = 4 or k = 1 .