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Sia ? 6 years, 4 months ago
we have, 2x2 + 3x + k = 0.
a = 2, b = 3 and, c= k
The given equation will have real and equal roots, if
D = 0
{tex}\therefore{/tex} D = b2 - 4ac =0
{tex}\Rightarrow{/tex} 9 - 4 {tex}\times{/tex} 2 {tex}\times{/tex} k =0
{tex}\Rightarrow{/tex}9 - 8k = 0
{tex} \Rightarrow k= \frac { 9 } { 8 }{/tex}
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Sia ? 6 years, 4 months ago
If the squared difference of the zeroes of the quadratic polynomial f(x) = x2 + px + 45 is equal to 144, then ,we have to find the value of p.
Let {tex}\alpha{/tex} and {tex}\beta{/tex} be the zeroes of the given quadratic polynomial.
{tex}\therefore{/tex} {tex}\alpha{/tex} + {tex}\beta{/tex} = - p and {tex}\alpha\beta{/tex}= 45 ...(i)
Given, ({tex}\alpha{/tex} - {tex}\beta{/tex})2 = 144
or, ({tex}\alpha{/tex} + {tex}\beta{/tex})2- 4{tex}\alpha{/tex} {tex}\beta{/tex} = 144
or, (-p)2 - 4 {tex}\times{/tex} 45 = 144 [Using (i)]
p2 - 180 = 144
p2 = 144 + 180 = 324
{tex}\therefore{/tex} p = ± {tex}\sqrt{324}{/tex}= ± 18
Hence, the value of p is ± 18.
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Aditi Pathak 7 years, 7 months ago
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