Verify that 1 and 3/2 are the roots of the equation 2x2 – 5x + 3 = 0

1.	Verify that 1 and 3/2 are the roots of the equation 2x2 – 5x + 3 = 0.
Answer» Let the given Q.E. be p(x) = 2x² – 5x + 3 Now p(1) = 2(1)² – 5(1) + 3 = 2 – 5 + 3 = 0 ∴ 1 is a root of 2x² – 5x + 3 = 0 also p \((\frac{3}{2})\) = 2 \({(\frac{3}{2})}^2\) – 5 \((\frac{3}{2})\) + 3 = 2 × \(\frac{9}{4}\) – \(\frac{15}{2}\) + 3 = \(\frac{9}{2}\) + 3 – \(\frac{15}{2}\) = \(\frac{9+6-15}{2}\)= 0 ∴ \(\frac{3}{2}\) is also a root of 2x² – 5x + 3 = 0.

Verify that 1 and 3/2 are the roots of the equation 2x2 – 5x + 3 = 0.

Answer»

Let the given Q.E. be p(x) = 2x² – 5x + 3

Now p(1) = 2(1)² – 5(1) + 3

= 2 – 5 + 3 = 0

∴ 1 is a root of 2x² – 5x + 3 = 0

also p \((\frac{3}{2})\) = 2 \({(\frac{3}{2})}^2\) – 5 \((\frac{3}{2})\) + 3

= 2 × \(\frac{9}{4}\) – \(\frac{15}{2}\) + 3

= \(\frac{9}{2}\) + 3 – \(\frac{15}{2}\)

= \(\frac{9+6-15}{2}\)= 0

∴ \(\frac{3}{2}\) is also a root of 2x² – 5x + 3 = 0.