Question

3x²+2√5x-5=0
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Answer 1

Answer:

3x²+2√5x-5=0

3x²+3√5x-√5x-5=0

3x(x+√5)-√5(x+√5)=0

(x+√5)(3x-√5)=0

so x= -√5 and √5/3

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.