Question

In each of the following, determine whether the given numbers are roots of the given
equations or not:
(i) x2 – 5x + 6 = 0; 2,-3
(ii) 3x2 – 13x – 10 = 0; 5,-2/3
​

Answer 1

• 1st equation

$substituting \: value \: of \: x = 2 \\ we \: get \: \\ x {}^{2} - 5x + 6 = 0 \\ (2) {}^{2} - 5(2) = 0 - 6 \\ 4 - 10 = - 6 \\ - 6 = - 6 \: \\ hence \: the \: given \: no. \: is \: a \: root \: of \: eq {}^{n}$

$substituting \: value \: of \: x = - 3 \\ x {}^{2} - 5x + 6 = 0 \\ ( - 3) {}^{2} - 5( - 3) + 6 = 0 \\ 9 - 15 = - 6 \\ - 6 = - \\ hence \: 2 \: and \: - 3 \: are \: root \: of \: given \: eq {}^{n}$

• 2nd equation

$3x {}^{2} - 13x - 10 = 0 \\ subst. \: value \: of \: x = 5 \\ 3(5) {}^{2} - 13(5) - 10 = 0 \\ 75 - 65 = 10 = 10 \\ thus \: 5 \: is \: \: a \: root \: of \: eq {}^{n}$

$subs. \: value \: of \: x = \frac{ - 2}{3} \\ 3( \frac{ - 2}{3} ) {}^{2} - 13( \frac{ - 2}{3}) - 10 = 0$

$\frac{4}{3} + \frac{26}{3} = 10 \\ \frac{30}{3} = 10 \\ 10 = 10 \\ hence \: both \: no. \: are \: root \: of \: eq {}^{n} \\ i \: have \: used \: \\ eq {}^{n} \: instead \: of \: equation \\ and \: \\ \: subst. \: instead \: of \: substituting \\ hope \: it \: helps$