The value of - C - for which -2-2-7-4- where - and - are the roots of 2 x 2-7 x - c -0- isA- 6B- 2C- 0D- 4

The correct option is A 6 We have α + β=7/2 and αβ = c/2 ∴ |α^2 β^2|=7/4⇒α^2 β^2 = ±7/4 ⇒ (α + β)(α β)= ±7/4⇒ 7/2√(49/4 2c)= ±7/4 ⇒√(49 8c)=∓ 1 ⇒ 49 8c=1 ⇒ c= ...

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Standard XII

Mathematics

Integration of Piecewise Continuous Functions

The value of ...

Question

The value of ‘C’ for which $| α^{2} - β^{2} | = \frac{7}{4}$ , where $α$ and $β$ are the roots of $2 x^{2}$ +7x + c = 0 , is

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Solution

The correct option is C
6

We have $α + β = \frac{7}{2} a n d α β = \frac{c}{2}$

$∴ | α^{2} - β^{2} | = \frac{7}{4} \Rightarrow α^{2} - β^{2} = \pm \frac{7}{4} \Rightarrow (α + β) (α - β) = \pm \frac{7}{4} \Rightarrow - \frac{7}{2} \sqrt{\frac{49}{4} - 2 c} = \pm \frac{7}{4} \Rightarrow \sqrt{49 - 8 c} = \mp 1 \Rightarrow 49 - 8 c = 1 \Rightarrow c = 6$

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The value of ‘C’ for which |α2−β2|=74 , where α and β are the roots of 2x2+7x + c = 0 , is

The correct option is C 6 We have α+β=72 and αβ=c2 ∴ |α2−β2|=74⇒α2−β2=±74⇒(α+β)(α−β)=±74⇒−72√494−2c=±74⇒√49−8c=∓1⇒49−8c=1⇒c=6

The value of ‘C’ for which $| α^{2} - β^{2} | = \frac{7}{4}$ , where $α$ and $β$ are the roots of $2 x^{2}$ +7x + c = 0 , is