Question

answer these please. ​

Answer 1

Step-by-step explanation:

13)

The given equation has equal roots, so discriminant is zero.

So,

$2 {x}^{2} + kx + 3 = 0 \\ {k}^{2} - 4(3)(2) = 0 \\ {k}^{2} = 24 \\ k = 2 \sqrt{6} \: or \: k = - 2 \sqrt{6}$

14)

The AP is 7, 13, 19 ... 205

So, a=7, d=13-7=6 and a(n)=205

a(n)=a+(n-1)d

205=7+(n-1)6

198=(n-1)6

n-1=33

n=34

There are 34 terms in the AP.

Thank you

Answer 2

Answer:

so n=34

Step-by-step explanation:

The AP is 7, 13, 19 ... 205

So, a=7, d=13-7=6 and a(n)=205

a(n)=a+(n-1)d

205=7+(n-1)6

198=(n-1)6

n-1=33

n=34

There are 34 terms in the AP.