What will be the difference of the cube and square of the common root of
$x^{2} + 4 x - 21 = 0$ and $y^{2} + 15 y - 54 = 0$ ?

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294

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392

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Solution

The correct option is C 36
Roots of $x^{2}$ + 4x - 21 = 0 are -3 or 7
Roots of $y^{2}$ + 15y - 54 = 0 are -3 or 18
So, the common root is -3
$(- 3)^{2}$ - $(- 3)^{3}$ = 9 - -27 = 36

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Similar questions

Find the equation of circle which touches $2 x - y + 3 = 0$ and pass through the points of intersection of the line $x + 2 y - 1 = 0$ and the circle $x^{2} + y^{2} - 2 x + 1 = 0$

Q. Find the transverse common tangents of the circle

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and

x^{2} + y^{2} + 4 x - 6 y + 4 = 0

Q. Find the transverse common tangents of the circles:

x^{2} + y^{2} - 4 x - 10 y + 28 = 0

and

x^{2} + y^{2} + 4 x - 6 y + 4 = 0

Find the equation of pair of tangents drawn to the circle $x^{2} + y^{2} - 4 x + 4 y = 0$ from the point (2, 2)

Q. I : The equations to the direct common tangents to the circles

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y - 1 = 0

4 x - 3 y - 9 = 0

II : The equations to the transverse common tangents to the circles

x^{2} + y^{2} - 4 x - 10 y + 28 = 0

x^{2} + y^{2} + 4 x - 6 y + 4 = 0

are

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What will be the difference of the cube and square of the common root of x2+4x−21=0 and y2+15y−54=0 ?

The correct option is C 36Roots of x2 + 4x - 21 = 0 are -3 or 7 Roots of y2 + 15y - 54 = 0 are -3 or 18 So, the common root is -3 (−3)2 - (−3)3 = 9 - -27 = 36

What will be the difference of the cube and square of the common root of
$x^{2} + 4 x - 21 = 0$ and $y^{2} + 15 y - 54 = 0$ ?

The correct option is C 36
Roots of $x^{2}$ + 4x - 21 = 0 are -3 or 7
Roots of $y^{2}$ + 15y - 54 = 0 are -3 or 18
So, the common root is -3
$(- 3)^{2}$ - $(- 3)^{3}$ = 9 - -27 = 36