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Worked solution

Classify roots without solving the equation

Determine the nature of the roots of the equation 4x2+6x−1=04x^2+6x-1=0.

CJC · O Level revision · Example 3

Answer

The two roots are real and distinct.

Compare your reasoning

Evaluate the discriminant

D=b2−4ac=62−4(4)(−1)=52>0\begin{aligned}&D\\ & =b^2-4ac\\ & =6^2-4(4)(-1)\\ & =52>0\end{aligned}

A positive discriminant gives two distinct real roots, matching two x-axis crossings.

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