Given 6x^2 5x 25=0 First, let us find α and β such that α + β = 5 and αβ #160;= 6 × ( 25) = 150 , where 5 is the coeffici ...

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Zeroes of a Polynomial

Solve 6x2-5...

Question

Solve $6 x^{2} - 5 x - 25 = 0$

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Solution

Given $6 x^{2} - 5 x - 25 = 0$
First, let us find $α$ and $β$ such that $α + β = - 5$ and $α β = 6 \times (- 25) = - 150$ , where $- 5$ is the coefficient of x.
Thus, we get $α = - 15$ and $b = 10$ .
Next, $6 x^{2} - 5 x - 25 = 6 x^{2} - 15 x + 10 x - 25 = 3 x (2 x - 5) + 5 (2 x - 5)$
$= (2 x - 5) (3 x + 5)$
Therefore, the solution set is obtained from $2 x - 5 = 0$ and $3 x + 5 = 0$
Thus, $x = \frac{5}{2}, x = - \frac{5}{3}$
Hence, solution set is ${- \frac{5}{3}, \frac{5}{2}}$

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