Q. 24.2( 225 Votes )

# For what values of k, the roots of equation x^{2} + 4x + k = 0 are real?

Or

Find the value of k for which the roots of equation 3x^{2} – 10x + k = 0 are reciprocal of each other?

Answer :

For roots to be real D ≥ 0

⇒ b^{2} - 4ac ≥ 0

For x^{2} + 4x + k = 0,

^{2}- 4(1)k ≥ 0

⇒16 – 4k ≥ 0

⇒ – 4k ≥ - 16⇒4k ≤ 16

⇒k ≤ 4

Or

Consider 3x^{2} – 10x + k = 0,

Compare the given equation with the general equation ax^{2} + bx + c = 0

So, a = 3, b = -10, c = k

Let, the roots of the equation be x and 1/x.

Product of the roots

⇒ k = 3

Rate this question :

(x^{2} + 1)^{2} - x^{2} = 0 has

Find the value of p for which the quadratic equation

x^{2} – 2px + 1 = 0 has no real roots.

For what values of p are the roots of the equation 4 x^{2} + px + 3 = 0 real and equal?

Find the values of k for which the quadratic equation (k+4) x^{2} + (k+1) x + 1 = 0 has equal roots. Also, find these roots.

Find the value of p for which the quadratic equation = 0 has equal roots. Also, find these roots.

Mathematics - Board PapersIf 1 is a root of the quadratic equation and the quadratic equation has equal roots, find the value of b.

RD Sharma - MathematicsShow that the equation has no real roots, when .

RD Sharma - MathematicsIn the following, determine the set of values of k for which the given quadratic equation has real roots:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

RD Sharma - Mathematics