Question

The graph of the polynomial 4x^2-8x+3 cuts the x-axis at ________ and ________ points.

(a) (\(\frac {3}{4}\), 0), (\(\frac {1}{2}\), 0)

(b) (\(\frac {3}{2}\), 0), (\(\frac {1}{2}\), 0)

(c) (\(\frac {3}{2}\), 0), (\(\frac {1}{6}\), 0)

(d) (\(\frac {7}{2}\), 0), (\(\frac {3}{2}\), 0)

I got this question in exam.

My question is taken from Geometrical Meaning of Zeros of Polynomial in division Polynomials of Mathematics – Class 10

Answer 1

Right answer is (b) (\(\frac {3}{2}\), 0), (\(\frac {1}{2}\), 0)

Easy explanation: The graph of the polynomial cuts the x-axis. Only the zeros of the polynomial cut the x-axis.

4x^2-8x+3=0

4x^2-6x-2x+3=0

2x(2x-3)-1(2x-3)=0

(2x-3)(2x-1)=0

x=\(\frac {3}{2}, \frac {1}{2}\)

Hence, the graph of the polynomial cuts the x-axis at (\(\frac {3}{2}\), 0) and (\(\frac {1}{2}\), 0).