Question

Find the value of K for which following equation

has real and equal roots 4x²+Kx+9
pls give step by step explanation.​

Answer 1

Given :-

• 4x² + Kx + 9
• It has real and equal roots.

To find :-

• Value of K

Solution with explanation :-

✯ Comparing 4x² + Kx + 9 with ax² + bx + c. We get

• a = 4
• b = K
• c = 9

✯ By using Discrimininant formula that is

${ \large{ \bf{Discrimininant \: D = b^2-4ac }}}$

✯ Discrimininant :-

${\sf{\implies{b^2 - 4ac}}}$

${\sf{\implies{(k)^2 - 4(4)(9)}}}$

${\sf{\implies{k^{2} -144}}}$

✯ If we put D = 0 then value of k is :-

${\sf{\implies{k^{2} -144 = 0}}}$

${\sf{\implies{k^{2} = 144}}}$

${\sf{\implies{k = \sqrt{144} }}}$

${ \large{ \underline{ \overline{ \boxed{\bf{\implies{k = \pm 12 }}}}}}}$

So, value of k is 12 and -12 when it has real and equal roots.

Answer 2

Step-by-step explanation:

4x² + Kx + 9

It has real and equal roots.

To find :-

Value of K

Solution with explanation :-

✯ Comparing 4x² + Kx + 9 with ax² + bx + c. We get

a = 4

b = K

c = 9

✯ By using Discrimininant formula that is

{ \large{ \bf{Discrimininant \: D = b^2-4ac }}}DiscrimininantD=b

2

−4ac

✯ Discrimininant :-

{\sf{\implies{b^2 - 4ac}}}⟹b

2

−4ac

{\sf{\implies{(k)^2 - 4(4)(9)}}}⟹(k)

2

−4(4)(9)

{\sf{\implies{k^{2} -144}}}⟹k

2

−144

✯ If we put D = 0 then value of k is :-

{\sf{\implies{k^{2} -144 = 0}}}⟹k

2

−144=0

{\sf{\implies{k^{2} = 144}}}⟹k

2

=144

{\sf{\implies{k = \sqrt{144} }}}⟹k=

144

{ \large{ \underline{ \overline{ \boxed{\bf{\implies{k = \pm 12 }}}}}}}

⟹k=±12

So, value of k is 12 and -12 when it has real and equal roots.