# Algeb

• May 28th 2012, 07:10 AM
srirahulan
Algeb
if the quadratic equation$\displaystyle 2x^2-qx+r=0$have the roots $\displaystyle (\alpha+1),(\beta+2)$find out the value of q,r in terms of b,c.$\displaystyle x^2-bx+c=0$the quadratic equation have the real roots $\displaystyle \alpha,\beta$ and also $\displaystyle \ \alpha\geq\beta$if $\displaystyle \ \alpha=\beta$prove $\displaystyle q^2=4(2r+1)$
• May 28th 2012, 07:37 AM
Plato
Re: Algeb
Quote:

Originally Posted by srirahulan
if the quadratic equation$\displaystyle 2x^2-qx+r=0$have the roots $\displaystyle (\alpha+1),(\beta+2)$find out the value of q,r in terms of b,c.$\displaystyle x^2-bx+c=0$the quadratic equation have the real roots $\displaystyle \alpha,\beta$ and also $\displaystyle \ \alpha\geq\beta$if $\displaystyle \ \alpha=\beta$prove $\displaystyle q^2=4(2r+1)$

Using the product of the roots we get $\displaystyle (\alpha +1)(\beta +2)=\frac{r}{2}$ and $\displaystyle (\alpha)(\beta)=c$

Using the sum of the roots we get $\displaystyle \alpha +\beta+3 =\frac{q}{2}$ and $\displaystyle \alpha +\beta=b$