Advertisements
Advertisements
Question
Find the values of k for which the roots are real and equal in each of the following equation:
(2k + 1)x2 + 2(k + 3)x + (k + 5) = 0
Solution
The given quadric equation is (2k + 1)x2 + 2(k + 3)x + k + 5 = 0, and roots are real and equal
Then find the value of k.
Here,
a = (2k + 1), b = 2(k + 3) and c = k + 5
As we know that D = b2 - 4ac
Putting the value of a = (2k + 1), b = 2(k + 3) and c = k + 5
={2(k + 3)}2 - 4 x (2k + 1) x (k + 5)
= {4(k2 + 6k + 9)} - 4(2k2 + 11k + 5)
= 4k2 + 24k + 36 - 8k2 - 44k - 20
= -4k2 - 20k + 16
The given equation will have real and equal roots, if D = 0
-4k2 - 20k + 16 = 0
-4(k2 + 5k - 4) = 0
k2 + 5k - 4 = 0
Now factorizing the above equation
k2 + 5k - 4
`k=(-b+-sqrt(b^2-4ac))/(2a)`
`k=(-5+-sqrt(25+16))/2`
`k=-5+-sqrt41/2`
So, either
Therefore, the value of `k=-5+-sqrt41/2`
APPEARS IN
RELATED QUESTIONS
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
What is the value of discriminant for the quadratic equation X2 – 2X – 3 = 0?
If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.
(m – 12)x2 + 2(m – 12)x + 2 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`
Find the value of 'p' for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
