If alpha and beta are the …
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Sia ? 6 years, 7 months ago
The given quadratic polynomial is 2x2 + 5x + k.
If {tex}\alpha, \beta{/tex} are zeroes of quadratic polynomial
{tex}\alpha + \beta= \frac { - b } { a } = \frac { - 5 } { 2 } {/tex}
{tex} \alpha \beta= \frac { c } { a } = \frac { k } { 2 }{/tex}
Putting these values in {tex}( \alpha + \beta ) ^ { 2 } - \alpha \beta{/tex} = 24,
we get {tex}\left( \frac { - 5 } { 2 } \right) ^ { 2 } - \frac { k } { 2 } = 24 {/tex}
{tex}\Rightarrow \frac { 25 } { 4 } - \frac { k } { 2 } = 24{/tex}
{tex}\Rightarrow\frac { - k } { 2 } = 24 - \frac { 25 } { 4 }{/tex}
{tex}\Rightarrow \frac { - k } { 2 } = \frac { 96 - 25 } { 4 }{/tex}
{tex}\Rightarrow k = \frac { - 71 } { 4 } \times 2 = \frac { - 71 } { 2 }{/tex}
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