Question

4. If the roots of the quadratic equation
${x}^{2} + 6x + k = 0$
are equal then the value of k is
​

Answer 1

Step-by-step explanation:

x^2+6x+k=0

x^2+3x+3x+k=0

x(x+3)+3(x+k/3)

roots are equal so

x+3=x+ k/3

3=k/3

k=9

Answer 2

Given

A quadratic equation : x²+6x+k=0

To find

We have to find the value of k

$\sf\huge {\underline{\underline{{Solution}}}}$

Since ,the roots of the quadratic equation are equal then the discriminant must be equal to zero.e.g.,=> b²-4ac=0

Discriminant = b²-4ac

x²+6x+k=0

a= 1;b= 6 & c= k

=>b²-4ac=0

=> (6)²-4(1)(k)=0

=> 36-4k=0

=> -4k= -36

=> k= 9

Hence,the value of k is 9

_______________________________

Check:

=> x²+6x+9

=>x²+3x+3x+9

=> x(x+3)+3(x+3)=0

=> (x+3)(x+3)=0

Since,both are same.

Therefore,the Equation have two equal roots.

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More information=>

• If the discriminant b²-4ac is > 0 then there will be two real roots .
• If the discriminant b²-4ac is < 0 then there will be 2 complex roots.