Math, asked by rishabswaroop, 1 year ago

Need Help in Q.23 (BOTTOM CORNER)

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Answered by shruti216619

P = -2
and the given equation has equal roots.
then,d=0

rishabswaroop: Heyy even I got the same thing but the answer is wrong

rishabswaroop: The answer is
K = -10/9 and 2

shruti216619: may be the given answer is incorrect

ashish010603: The answer is wrong because x = -4 is only for the first equation, not for the quadratic equation.

ashish010603: The Answer is k = -10/9, 2

rishabswaroop: Yup

rishabswaroop: Can You show how to do it?

ashish010603: I've added the answer, hope you will find it easy

Answered by ashish010603

p(x) = x² + 2x + 4p

p(-4) = 0

⇒ (-4)² + 2(-4) + 4p = 0

⇒ 16 - 8 = -4p

⇒ p = -2

Now, Given quadratic equation:

x² +px(1+3k) + 7(3+2k) = 0

⇒ x² -2(1+3k)x + 7(3+2k) = 0 [ a = 1, b = -2(1+3k), c = 7(3+2k) ]

Discriminant = 0, since the equation has equal roots

. : b² - 4ac = 0

⇒ [ -2 -6k]² -4(7)(3+2k) = 0

⇒ 4 + 36k² + 24k - 56k -84 = 0

⇒ 36k² - 32k -80 = 0

⇒ 9k² - 8k - 20 = 0

⇒ 9k² - 18k + 10k - 20 = 0

⇒ (9k + 10)(k - 2) = 0

⇒ k = -10/9 (or) k = 2

rishabswaroop: Thanks man

ashish010603: Welcome dude...

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