Question

10. The length of x-intercept made by pair of lines
2x ^2+ xy - 6y^2 - 2 x+ 17y - 12=0
​

Answer 1

The length of the x-intercept is 5 units.

Given:

A pair of lines $2x^{2} +xy-6y^{2} -2x+17y-12=0$

To Find:

The length of the x-intercept made by the given lines

Solution:

We can simply solve this problem by using the following mathematical process.

Putting y = 0 in the given pair of lines we have,

$2x^{2} -2x-12=0$

Using the formula to find the roots of the equation $x_{1} =\frac{-b+\sqrt{b^{2} -4ac} }{2a}$ and $x_{2} =\frac{-b-\sqrt{b^{2} -4ac} }{2a}$

We get,

$x_{1} =\frac{2+\sqrt{(-2)^{2} -4(2)(-12)} }{2(2)}$ and $x_{2} =\frac{2-\sqrt{(-2)^{2} -4(2)(-12)} }{2(2)}$

$x_{1} =\frac{2+\sqrt{100} }{4}$ and $x_{2} =\frac{2-\sqrt{100} }{4}$

$x_{1} =3$ and $x_{2} =-2$

Now,

$x_{1} -x_{2}=5$

Therefore, the length of the x-intercept is 5 units.

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