Question

solve this question​

Answer 1

Given:-

→p(x)=2x²+5x+k

→(α+β)²-αβ=24

$\rule{200}{1}$

To Find:-

→The Value of k?

$\rule{200}{1}$

AnsWer:-

♦a=2,b=5,c=k

→α+β=$\frac{-b}{a}$

→α+β=$\frac{-(5)}{2}$

→α+β=$\frac{-5}{2}$–(1)

•αβ=$\frac{c}{a}$

•αβ=$\frac{k}{2}$–(2)

๛Using (1) & (2) in Given๛

→(α+β)²-αβ=24

→($\frac{-5}{2}$)²-$\frac{k}{2}$=24

→$\frac{25}{4}$-$\frac{2 \times k}{2 \times 2}$=24

→$\frac{25-2k}{4}$=24

→25-2k=24×4

→25-2k=96

→-2k=96-25

→-2k=71

→-k=$\frac{71}{2}$

→k=$\frac{\cancel{-71}}{\cancel{2}}$

→k=-35.5

$\rule{200}{2}$

Answer 2

Answer....

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$2 {x}^{2} + 5x + k \\ \\ ................. \\ \\ {(\alpha + \beta )}^{2} - \alpha \beta = 24 \\ \\ = > { ( \frac{ - b}{a} )}^{2} - (\frac{c}{a} ) = 24 \\ \\ = > { ( \frac{ - 5}{2} )}^{2} - (\frac{k}{2} ) = 24 \\ \\ = > \frac{25}{4} - \frac{k}{2} = 24 \\ \\ = > \frac{25 - 2k}{4} = 24 \\ \\ = > 25 - 2k = 96 \\ \\ = > - 2k = 96 - 25 \\ \\ = > - 2k = 71 \\ \\ = > k = \frac{ - 71}{2}$

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Hope you got it