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Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=5x^2–7x+12.

User FlimFlam Vir
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1 Answer

14 votes
14 votes

Consider the general case


ax^2+bx+c=0

This equation has the solutions


x=\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}

In here, the quantity


b^2-4ac

is called the discriminant. If the discriminant is greater than or equal to zero, then the roots of the equation are real. If the discriminant is negative, the roots are imaginary (complex roots).

In our case 5x^2-7x+12, a=5,b=-7,c=12. Then, the discrimininant is


b^2-4ac=(-7)^2-4\cdot5\cdot12\text{ = 49-240 = -191<0}

This means that the roots of this equation are all imaginary (complex).

User JRB
by
2.9k points
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