Question

please solve 7th. do it fast.

Answer 1

Hey!!

Let's Solve

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let p(x) = 2x² - 5x + k

We know

$= > \alpha + \beta = \frac{ - b}{a}$

Thus

$= > \alpha + \beta = \frac{5}{2}$

Similarly

$= > \alpha \beta = \frac{c}{a}$

$= > \alpha \beta = \frac{k}{2}$

Now

Condition

${( \alpha + \beta )}^{2} - \alpha \beta = 24$

Replacing value

$= > { (\frac{5}{2}) }^{2} - \frac{k}{2} = 24$

=> 25/4 - k/2 = 24

=> k/2 = 25/4 - 24

=> k/2 = (25 - 96)/2

Cancelling denominators

$= > k = \frac{ - 71}{2}$

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Hope this helps ✌️

Legally Good Morning :-)

Answer 2

α+β = -5/2
αβ = κ/2

(α+β)² - αβ = 24

(-5/2)² - κ/2 = 24

25/4 - 24 = κ/2

κ = -71/2