Determine the nature of the roots of the quadratic equation without solving it. $4 x ^ { 2 } - 7 x + 3 = 0$
A) two irrational roots
B) one rational root
C) two rational roots
D) two imaginary roots

Question

Determine the nature of the roots of the quadratic equation without solving it. $4 x ^ { 2 } - 7 x + 3 = 0$
A) two irrational roots
B) one rational root
C) two rational roots
D) two imaginary roots

Quizplus · Accepted Answer

We can use the discriminant, which is given by $b^2-4ac$, to determine the nature of the roots. In this case, $a=4$, $b=-7$, and $c=3$. Thus the discriminant is $( - 7 ) ^ { 2 } - 4 \cdot 4 \cdot 3 = 49 - 48 = 1$. Since the discriminant is positive and not a perfect square, the roots are two rational roots.

Determine the Nature of the Roots of the Quadratic Equation 4x2−7x+3=04 x ^ { 2 } - 7 x + 3 = 04x2−7x+3=0

Determine the Nature of the Roots of the Quadratic Equation $4 x ^ { 2 } - 7 x + 3 = 0$