SOLUTION: Okay, I really need an understanding on Quadratics. Could some one help me understand this problem?
The instructions are to: Use the discriminate to determine whether this quadr
Question 18720: Okay, I really need an understanding on Quadratics. Could some one help me understand this problem?
The instructions are to: Use the discriminate to determine whether this quadratic polynomial can be factored, factor the numbe is it is not prime.
8x^2 - 10x - 3
Thank you all for the help!
You can put this solution on YOUR website! Use the discriminate to determine whether this quadratic polynomial can be factored, factor the numbe is it is not prime.
8x^2 - 10x - 3
the roots or values of x which satisfy the following quadratic equation ( called a solution for the eqn) ax^2+bx+c=0 is given by the formula ..
here we find the critical term which determines the nature of solution is the term under square root namely
b^2-4ac which is called the discriminant (D in short)
if D is -ve the square root becomes imaginary...then there are no roots.
if D=0,we will have 2 equal roots or..the expression will be a perfect square.
if D>0 and a perfect square .then we will have 2 distinct rational roots.
if D>0 ,but not a perfect square we will have 2 distinct irrational roots
here in your example we have D=(-10)^2-4*8*(-3)=100+96=196 which is positive and perfect square (14*14=196)..so it will have 2 distinct rational roots ..you can find them by using the above formula..once you find the 2 roots as say p and q then the given equation can be factored and written as {EQUIVALENT} to
(x-p)*(x-q)=0...in the above example we get p=3/2 and q=-1/4...so
8x^2-10x-3=0 is EQUIVALENT to (x-3/2)(x+1/4)=0...NOTE THAT THE TWO EXPRESSIONS GIVEN BY 8x^2-10x-3 and (x-3/2)(x+1/4) are not same but theeir equations with zero {8x^2-10x-3=0 and (x-3/2)(x+1/4)=0.}gives the same solution set of
x=3/2 or -1/4..hence they are called equivalent but not same expression.if you want the same expression you have to find a constant say k which when multiplied with gives same expressions .here we find that k=8 since
8x^2-10x-3=8(x-3/2)(x+1/4)=4*2(x-3/2)(x+1/4)=2(x-3/2)*4(x+1/4)=(2x-3)(4x+1)=
8x^2-10x-3
