Write a quadratic equation with -3/4 and 4 as its roots. Write the equation in form ax^2+bx+c=0, where a,b,and c are integers.
(x-p)(x-q)=0
(x--3/4)(x-4)=0
(x+3/4)(x-4)=0
x^2-3x+3=0(answer)
if the roots are -3/4 and 4 then the factors that will form your equation are
(4x+3) and (x-4)
so (4x+3)(x-4) = 0 or
4x^2 13x - 12 = 0
(x+3/4)(x-4)=x²+3/4x-4x-3=x²-(13/4)x-3
if u want to know if your answer is right or false, it's easy
f(x)=x²-(13/4)x-3
and u can verify if f(4)=0 and f(-3/4)=0
To clarify, the correct quadratic equation with -3/4 and 4 as its roots is given by:
(x + 3/4)(x - 4) = 0
To expand this, you need to apply the FOIL method (First, Outer, Inner, Last):
x(x) + x(-4) + (3/4)(x) + (3/4)(-4) = 0
This simplifies to:
x^2 - 4x + (3/4)x - 3 = 0
Combining like terms:
x^2 - (13/4)x - 3 = 0
Therefore, the quadratic equation in the required form is:
x^2 - (13/4)x - 3 = 0
To write a quadratic equation with -3/4 and 4 as its roots, we need to use the fact that when a quadratic equation is in the form (x - p)(x - q) = 0, where p and q are the roots, then we can expand this equation to obtain the quadratic equation.
In this case, the given roots are -3/4 and 4. Therefore, we can write the equation as follows:
(x - (-3/4))(x - 4) = 0
Now, let's simplify this equation:
(x + 3/4)(x - 4) = 0
To expand this equation, we can use the distributive property. Multiply each term in the first set of parentheses by each term in the second set of parentheses:
x * x + x * (-4) + (3/4) * x + (3/4) * (-4) = 0
x^2 - 4x + (3/4)x - 3 = 0
Now, let's combine like terms:
x^2 - 4x + (3/4)x - 3 = 0
Rewriting the equation as a quadratic equation in the form ax^2 + bx + c = 0, we get:
x^2 - (4 - 3/4)x - 3 = 0
Simplifying further, we have:
x^2 - (16/4 - 3/4)x - 3 = 0
x^2 - (13/4)x - 3 = 0
Therefore, the quadratic equation with roots -3/4 and 4 is:
x^2 - (13/4)x - 3 = 0