Posted by Drake on Wednesday, June 26, 2013 at 10:41am.
If the quadratic equation for x
has real roots, what is the value of
- Math (Quadratics) - Steve, Wednesday, June 26, 2013 at 11:25am
the discriminant must not be negative, so
4(2a+2b+1)^2 - 4*5(1+(a+b)^2) >= 0
a^2 + 2ab + b^2 - 4(a+b) + 4 >= 0
(a+b)^2 - 4(a+b) + 4 >= 0
((a+b)-2)^2 >= 0
Hmmm. That's true for any a,b.
If a+b=2, then the original equation has a repeated root and
a^3+b^3+6ab+a+b = (a+b)(a^2-ab+b^2) + (a+b) + 6ab
= (a+b)(a^2+b^2+1) + ab(6-(a+b))
= 2(a^2+b^2+1) + ab(6-2)
= 2a^2+2b^2+2 + 4ab
= 2(a+b)^2 + 2
Haven't yet worked it out for other a,b but the wording of the question makes me believe the expression is 10 for any a,b.
Answer This Question
More Related Questions
- algerba - What is the value of the discriminant, b2 − 4ac, for the ...
- algebra - if a quadratic equation with real coefficents has a discriminant of 10...
- Math - Determine for what value(s) of d the quadratic equation 5x^2-10x+d = 0 ...
- Precalculus - "Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the ...
- Math - determine the value(s) of k which a quadratic equation x^2+kx+9=0 will ...
- Math (Algebra) - If the ratio of the roots of the quadratic equation x^2−...
- Algebra 2(quadratic) - Use the value of the discriminant to determine the number...
- maths - If the quadratic equation (8+i)x^2+(a-i)x+38-2i=0 has real roots, what ...
- Maths - There are two complex roots to the quadratic equation z^2 +(1−16i)...
- Algebra2 - Find the polynomials roots to each of the following problems: #1) x^2...