Question

Question in the Attachment ​

Answer 1

$\bf{Question-}$

Determine k such that the quadratic equation x² +7(3+2k)-2x (1+3k) = 0 has equal roots:

(a) 2, 7

(b) 7, 5

(c) 2

(d) -10/9

$\bf{Solution-}$

As we know that For the quadratic equation to have equal roots discriminant should be zero

$\:\:\:\implies$ {-2(1+3k)}² − 4(1){7(3+2k)} = 0

$\:\:\:\implies$ 4(1 + 3k)² - 28(3 + 2k) = 0

$\:\:\:\implies$ (9k2 + 6k+1) - 21 - 14k = 0

$\:\:\:\implies$ 9k²- 8k - 20 = 0

$\:\:\:\implies$ 9k² + 18k+ 10k - 20 = 0

$\:\:\:\implies$ 9k(k − 2) + 10(k − 2) = 0

$\:\:\:\implies$ (9k + 10) (k − 2) = 0

$\:\:\:\implies$ (9k + 10) = 0, (k − 2) = 0

$\:\:\:\implies{\boxed{\bf{k = -\frac{10}{9}, 2}}}$

Answer 2

Answer:

Question−

Determine k such that the quadratic equation x² +7(3+2k)-2x (1+3k) = 0 has equal roots:

(a) 2, 7

(b) 7, 5

(c) 2

(d) -10/9

\bf{Solution-}Solution−

As we know that For the quadratic equation to have equal roots discriminant should be zero

\:\:\:\implies⟹ {-2(1+3k)}² − 4(1){7(3+2k)} = 0

\:\:\:\implies⟹ 4(1 + 3k)² - 28(3 + 2k) = 0

\:\:\:\implies⟹ (9k2 + 6k+1) - 21 - 14k = 0

\:\:\:\implies⟹ 9k²- 8k - 20 = 0

\:\:\:\implies⟹ 9k² + 18k+ 10k - 20 = 0

\:\:\:\implies⟹ 9k(k − 2) + 10(k − 2) = 0

\:\:\:\implies⟹ (9k + 10) (k − 2) = 0

\:\:\:\implies⟹ (9k + 10) = 0, (k − 2) = 0

\:\:\:\implies{\boxed{\bf{k = -\frac{10}{9}, 2}}}⟹k=−910,2

hope it may help you