For a given value of k, the product of the roots of x2 - 2kx + 3k2 - 4 = 0 is 5. The roots may be characterised as

Question

For a given value of k, the product of the roots of x2 - 2kx + 3k2 - 4 = 0 is 5. The roots may be characterised as (A) integral (B) rational but not integral (C) irrational (D) imaginary

Tardigrade Admin · Accepted Answer

Since product of the roots = 5. ∴ 3 k2 - 4 = 5 ⇒ 3 k2 = 9 ⇒ k2 = 3. Now Disc. = 4k2 - 4(3k2 - 4) = 16 - 8 k2 = 16 - 24 = - 8 < 0 ∴ roots are imaginary.

Q. For a given value of $k$ , the product of the roots of $x^{2} - 2 k x + 3 k^{2} - 4 = 0$ is $5$ . The roots may be characterised as

integral

rational but not integral

irrational

imaginary

Since product of the roots $= 5$ .
$∴ 3 k^{2} - 4 = 5$
$\Rightarrow 3 k^{2} = 9$
$\Rightarrow k^{2} = 3$ .
Now Disc. $= 4 k^{2} - 4 (3 k^{2} - 4) = 16 - 8 k^{2}$
$= 16 - 24 = - 8 < 0$
$∴$ roots are imaginary.

Q. For a given value of k, the product of the roots of x2−2kx+3k2−4=0 is 5. The roots may be characterised as