Question

Determine the value(s) of n so that the quadratic relation y=x^2+nx+16 has only one zero.

Answer 1

Answer:

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Answer 2

Answer:

A number(s) is the zero(es) of a function when y=0 .

∴ The quadratic function has only 1 zero means that −nx2+4x−1=0 has only 1 solution.Hence the value of the 2 roots of the equation α and β are equal ie α=β .

∴D=b2–4ac=0

⇒42–4(−n)(−1)=0

⇒−4n=−16

⇒n=4

To verify the answer, substitute n=4 in −nx2+4x−1=0 ,then multiply negative both sides,then factorize the LHS and you will get ( 2x−1)2=0

⇒(2x−1)(2x−1)=0 .Here ,in both cases we get x=12 ie for n=4 , the quadratic function has only 1 zero.