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Sia ? 6 years, 6 months ago
Let {tex} \alpha{/tex} and {tex} \frac { 1 } { \alpha }{/tex} be the zeros of (a2 + 9)x2 + 13x + 6a.
Then, we have
{tex} \alpha \times \frac { 1 } { \alpha } = \frac { 6 a } { a ^ { 2 } + 9 }{/tex}
⇒ 1 = {tex} \frac { 6 a } { a ^ { 2 } + 9 }{/tex}
⇒ a2 + 9 = 6a
⇒ a2 - 6a + 9 = 0
⇒ a2 - 3a - 3a + 9 = 0
⇒ a(a - 3) - 3(a - 3) = 0
⇒ (a - 3) (a - 3) = 0
⇒ (a - 3)2 = 0
⇒ a - 3 = 0
⇒ a = 3
So, the value of a in given polynomial is 3.
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Sia ? 6 years, 6 months ago
p(x) = 5x2 + 8x - 4 = 0
= 5x2 + 10x - 2x - 4 = 0
= 5x(x + 2) - 2(x + 2) = 0
= (x + 2)(5x - 2) = 0
Hence, zeroes are -2 and {tex}\frac 25{/tex}
Verification:
Sum of zeroes = {tex}- 2 + \frac { 2 } { 5 } = \frac { - 8 } { 5 }{/tex}
Product of zeroes = {tex}( - 2 ) \times \left( \frac { 2 } { 5 } \right) = \frac { - 4 } { 5 }{/tex}
Again sum of zeroes = {tex}- \frac { \text { Coeff. of } x } { \text { Coeff. of } x ^ { 2 } } = \frac { - 8 } { 5 }{/tex}
Product of zeroes = {tex}\frac { \text { Constant term } } { \text { Coeff. of } x ^ { 2 } }{/tex} = {tex}\frac{-4}{5}{/tex}
Verified.
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Sia ? 6 years, 6 months ago
{tex}\sqrt { 3 } x ^ { 2 } - 2 \sqrt { 2 } x - 2 \sqrt { 3 } = 0{/tex}
{tex}\sqrt { 3 } x ^ { 2 } - 3 \sqrt { 2 } x + \sqrt { 2 } x - 2 \sqrt { 3 } = 0{/tex}
{tex}\sqrt { 3 } x [ x - \sqrt { 6 } ] + \sqrt { 2 } [ x - \sqrt { 6 } ] = 0{/tex}
or, {tex}( x - \sqrt { 6 } ) ( \sqrt { 3 } x + \sqrt { 2 } ) = 0{/tex}
or, {tex}x = \sqrt { 6 } , - \sqrt { \frac { 2 } { 3 } }{/tex}

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Yathath Yadav 7 years, 3 months ago
7Thank You