If 3 is a root of the quadratic equation x2+ bx-15=0 determine the value of b. Find the value of the other root.
According to the remainder theorem of polynomials, ‘a’ is a root of a function f(x) if and only if f(a)=0.
3 is a root of it.
Put f(3) = 0 to get:
The given equation then simplifies to: `x^2+ 2x-15=0`.
The equation can also be written as: `x^2+ 5x-3x-15=0`
`rArr x(x+ 5)-3(x+5)=0`
So, the other root is -5.
If 3 is a root of the quadratic equation x^2+ bx-15=0 determine the value of b. Find the value of the other root.
Now according to the question, 3 is a root of the quadratic equation given.
And according to the Remainder theorem of Polynomials,
‘a’ is a root of a function f(x) if and only if f(a)=0.
With the help of this given root we will first find the value of b.
according to the equation;
a = 1
b = ?
c = 15
Now since we found out the value of b which is 2, now we will insert in the given equation and simplify it.
b = 2
The equation is: `f(x)=x^2+bx-15=0`
Insert the value of b in the equation and then simplify;
So the other root is -5.