SOLUTION: Show that for all real values of 'a' greater than 4,x Squared-2x+a=3 will have non-real roots

Question 1112242: Show that for all real values of 'a' greater than 4,x Squared-2x+a=3 will have non-real roots
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
in the quadratic formula one can look at the discriminate
to figure out what type of roots there will be:
If this value is negative, then the roots are complex (in conjugate pairs)
if this value is zero, then there is a real root, and it has multiplicity 2.
if the value is positive, then there are two unique real roots.

�> discriminate is =
Complex roots will occur when

�
Ans: Complex roots will occur when
�
��
Dear student,
I did not answer your question twice. The 'a' in the top part where I discuss the discriminate is from the standard form of a quadratic equation (a is the coefficient of the x^2 term) which I failed to write down for some reason. The 'a' in the question you posted is part of the constant term (c) in that expression.
To make it clear, let's re-write the question as follows: " For what values of 'v' does have non-real roots?"

Compare this with the standard form of the quadratic you will see a=1, b=-2, c=v-3 (here a,b,c refer to the standard form of the quadratic equation).
Now plug into the discriminate, D, D =
D =
D =
D = �> this means when 16-4v < 0 there are non-real (complex) roots.

16-4v < 0
16 < 4v
4 < v
v > 4 <<<< done. I used 'v' instead of 'a' to avoid confusion with the standard form of the quadratic equation.
I hope this helps.

RELATED QUESTIONS
Please help me answer this question: Show that for all real values of 'a' greater than 4. (answered by josgarithmetic)

Show that for all real values of a greater than 4,{{{x^2-2x a=3}}} will have nonreal... (answered by Fombitz)

Given that the equation x(x-2p)=q(x-p) has real roots for all real values of p and q. If... (answered by josgarithmetic,MathTherapy)

For which values of P will x^2+p+x=3(x+1) have real... (answered by mananth,LinnW,Theo)

For what real values of a does the quadratic 4x^2 + ax + 25 have non-real roots? Give... (answered by josmiceli)

All the roots of x^2 + px + q = 0 are real, where p and q are real numbers. Prove that... (answered by ikleyn)

Show that the roots of the equation (x-p)(x-q)=2 are real and distinct for all real... (answered by Edwin McCravy,ikleyn)

Find all real values of k for which 2x squared plus kx plus 3 equals 0 has a double... (answered by stanbon)

If f(x) = (3x + a), determine the values of 'a' for which, f(x2 + x + 2) - f(3x - a) = 0... (answered by josgarithmetic)