Question

Find the value of k for quadratic equation kx²+(2k+4)x+9=0,so that they have two equal roots. ​

Answer 1

Step-by-step explanation:

See attachment please

Answer 2

k=1 and k=4 are the two values of k for which they have equal roots.

• kx²+(2k+4)x+9=0 is the given quadratic equation.

• Now we know from the theory of equations that a quadratic equation of the form $ax^{2} +bx+c = 0$ will have equal roots if and only if $b^{2}=4ac$

• Hence (2k+4)^2 = 36k is the equation now
• Expanding and simplifying we get $k^{2} -5k+4=0$
• This leads to two values of k as 1 and 4
• Hence for k=1 and k=4 the quadratic equation kx²+(2k+4)x+9=0,have two equal roots. ​