Question

Solve these questions

Answer 1

★ Hey sister !! ★


here is your answer !!!



look at the attachment :-



hope it helps you dear !!!



hence , 1 ==> 1 / 4


2 ) 5 / 2


3 ====> 1





thanks !!!

Answer 2

Final Answer : 22 : k= 7/4
23 : k = 1
24 : m = 1

Steps:
22 :
1 ) Since, - 5 is one of zero of
$2 {x}^{2} + px - 15$
Therefor,
$2( { - 5)}^{2} + p \times ( - 5) - 15 = 0 \\ = > 50 - 5p - 15 = 0 \\ = > 5p = 35 = > p = 7$

Now, zeroes of p(x^2 + x) + k are equal.
px^2 + px+ k = 7x^2 + 7x+k
So,
D = 0
=>
${7}^{2} - 4 \times 7 \times k = 0 \\ = > k = \frac{7}{4}$


Steps:
23 :
$3 {x}^{2} + (2k + 1)x - (k + 5) = 0$
Sum of zeroes = 1/2 Product of zeroes
=>
$\frac{ - (2k + 1)}{3} = \frac{ - (k + 5)}{3} \times \frac{1}{2} \\ = > 4k + 2 = k + 5 \\ = > 3k = 3 \\ = > k = 1$

24: Given eq:


${y}^{2} + 5y + m$

And
$\alpha + \beta = - 5 \\ \alpha \beta = m$
And given is
${( \alpha + \beta )}^{2} - \alpha \beta = 24 \\ {( - 5)}^{2} - m = 24 \\ m = 25 - 24 = 1$