Advertisements
Advertisements
Question
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Advertisements
Solution
The given quadric equation is x2 + kx + 4 = 0, and roots are real.
Then find the value of k.
Here,
a = 1, b = k and c = 4
As we know that D = b2 − 4ac
Putting the value of a = 1, b = k and c = 4
= k2 − 4 × (1) × (4)
= k2 − 16
The given equation will have real and equal roots, if D = 0
k2 − 16 = 0
Now factorizing of the above equation
k2 − 16 = 0
k2 = 16
`k=sqrt16`
k = ± 4
Now according to question, the value of k is positive.
Therefore, the value of k = 4
APPEARS IN
RELATED QUESTIONS
If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x)k = 0 has equal roots, find the value of k.
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
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Solve the following quadratic equation using formula method only
15x2 - 28 = x
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
If a = 1, b = 8 and c = 15, then find the value of `"b"^2 - 4"ac"`
Find the value of k for which the given equation has real roots:
kx2 - 6x - 2 = 0
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
Find the discriminant of the following equations and hence find the nature of roots: 2x2 + 15x + 30 = 0
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0
Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x2 + (p – 3)x + p = 0.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
The roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then:
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
The roots of quadratic equation x2 – 1 = 0 are ______.
