Question

find the value of k for which the equation 4x2+kx+25 =0 has equal roots​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{4x^2+k\,x+25=0\;has\;equal\;roots}$

$\underline{\textbf{To find:}}$

$\textsf{The value of 'k'}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Concept used:}}$

$\textbf{Condition for the roots of the equation}\;\mathsf{ax^2+bx+c=0}\;\textbf{to be equal is}$

$\boxed{\mathsf{b^2-4ac=0}}$

$\mathsf{Consider,\;4x^2+k\,x+25=0}$

$\mathsf{Here,\;a=4,\;b=k,\;c=25}$

$\mathsf{Since\;the\;roots\;of\;4x^2+k\,x+25=0\;are\;equal,}$

$\mathsf{we\;have\;b^2-4ac=0}$

$\implies\mathsf{k^2-4{\times}4{\times}25=0}$

$\implies\mathsf{k^2-16{\times}25=0}$

$\implies\mathsf{k^2=16{\times}25}$

$\textsf{Taking square root on bothsies, we get}$

$\implies\mathsf{k=\pm(4{\times}5)}$

$\implies\mathsf{k=\pm\,20}$

$\underline{\textbf{Answer:}}$

$\mathsf{The\;values\;of\;k\;are\;\pm\,20}$

Answer 2

Answer:

+ or - 20

Step-by-step explanation:

Here we use the formula: b^2-4ac=0

In, 4x^2+kx+25

The coffecient of x is:

a=4, b=k, c=25

Now substitute the values in the formula...

k^2-4*4*25=0

k^2=16*25

Take square root on both sides , the square of k will get cancelled....

k=✓16*25

k=4*5

k=20

Therefore our answer is pluse or minus 20...

Thank you