SOLUTION: if r and s are the roots of the equation 2x^2-3x+4=o, what is 4r^2+7rs+4s^2?

SOLUTION: if r and s are the roots of the equation 2x^2-3x+4=o, what is 4r^2+7rs+4s^2?

Algebra.Com

Question 816668: if r and s are the roots of the equation 2x^2-3x+4=o, what is 4r^2+7rs+4s^2?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
2x^2-3x+4=o, what is 4r^2+7rs+4s^2
4r^2+7rs+4s^2
in the quadratic ax^2+bx+c=0 if p & q are the root of the equation
p+q=-b/a
pq=c/a
Similarly
in 2x^2-3x+4=o
r+s=3/2
rs=2
4r^2+7rs+4s^2
4r^2+8rs +4s^2 -8rs+7rs
(2r+2s)^2-rs
4(r+s)^2-rs
4(3/2)-2
6-2
=4

RELATED QUESTIONS
Suppose r and s are the roots of the quadratic equation 3x^2 + 2x - 8 = 0. Find the... (answered by ikleyn)

let the roots of the equation x^3 -2x^2 -3x-7=0 be r, s, and t. find the equation whose... (answered by math_tutor2020)

Suppose r and s are the roots of the quadratic equation 3x^2 + 2x - 8 = 0. Find the... (answered by ikleyn)

Let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 +... (answered by ikleyn)

If r=9 and 4r+3s=75, what is the value of... (answered by ewatrrr,Stitch)

Let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 +... (answered by ikleyn,Edwin McCravy,mccravyedwin)

Determine {{{(r + s)(s + t)(t + r)}}}, if r, s, and t are the three real roots of the... (answered by ikleyn)

if the roots of a quadratic equation are -4 and 2 the equation is equivalent to... (answered by josgarithmetic)

Can someone help me solve by the elimination method. 5r � 4s =2 4r +5s = 18 What is... (answered by MathLover1)