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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

If m1 and ...

Question

If $m_{1}$ and $m_{2}$ are the roots of the equation $x^{2} - a x - a - 1 = 0$ , then the area of the triangle formed by the three straight lines $y = m_{1} x, y = m_{2} x$ and $y = a (a \neq - 1)$ is

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Solution

Given equation: $x^{2} - a x - a - 1 = 0$
$x^{2} - (a + 1) x + x - (a + 1) = 0$
$(x - (a + 1)) (x + 1) = 0$
We get,
$x = a + 1$ and $x = - 1$
So, $m 1 = a + 1$ and $m 2 = - 1$
now, three lines are
$y = (a + 1) x . . . (i)$
$y = - x . . . (i i)$
$y = a . . . (i i i)$
on solving the three equations, we get three points that are (0, 0), (-a, a) and (a/(a+1),a) are of triangle formed by these three given points will be $a^{2} (a + 2) / (a + 1)$

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If m1 and m2 are the roots of the equation x2−ax−a−1=0, then the area of the triangle formed by the three straight lines y=m1x,y=m2x and y=a(a≠−1) is

If $m_{1}$ and $m_{2}$ are the roots of the equation $x^{2} - a x - a - 1 = 0$ , then the area of the triangle formed by the three straight lines $y = m_{1} x, y = m_{2} x$ and $y = a (a \neq - 1)$ is