Relationships between roots and coefficients (1 Viewer)

[Petinga]

Help needed ASAP

1. The roots of the quadratic equation ax^2 - bx - 10=0 are -1 and 5. Find the values of a and b.

2. One root of the equation x^2 + qx + r=0 is 3 times the other. Prove that 3q^2=16r

 

[香港!]

Help needed ASAP

1. The roots of the quadratic equation ax^2 - bx - 10=0 are -1 and 5. Find the values of a and b.

2. One root of the equation x^2 + qx + r=0 is 3 times the other. Prove that 3q^2=16r

1. a(-1)^2-b(-1)-10=0 and a(5)^2-b(5)-10=0
then solve simultaneous equations
2. let the roots be A and 3A
sum of roots, A+3A=4A=-q
so A=-q\4
product of roots, (A)(3A)=3A²=r

so 3(-q\4)²=r
3q²\16=r
3q²=16r

 

[Trev]

For question 1, I find it quicker to do these questions like this:
(x+1)(x-5)=0
x²-4x-5=0
2x²-8x-10=0
a=2; b=8.
Rather than doing simultaneous equations.