Question

For what value of k are the roots of the quadratic equation kxsquare+4x+1=0 equal and real?

Answer 1

GivEn:-

• Quadratic equation = kx² + 4x + 1 = 0

To find:-

• Value of k

SoluTion:-

• a = k

• b = 4

• c = 1

$\dag\;{\underline{\underline{\bf{According\;to\; Question:-}}}}$

The givEn equation has real and equal roots,

$\therefore$ b² - 4ac = 0

Substituting values in above formula,

$:\implies\sf (4)^2 - 4 \times k \times 1 = 0$

$:\implies\sf 16 - 4k = 0$

$:\implies\sf - 4k = - 16$

$:\implies\sf k = \cancel{ \dfrac{ 16}{ 4}}$

$:\implies{\underline{\boxed{\bf{\pink{k = 4}}}}}$

$\dag$ Hence, The value of k is 4.

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