If x 2 - 3x + 2 is a factor of x 3 - ax 2 + b, find the values of a and b.

Factorising, x 2 - 3x + 2. ⇒ x 2 - 2x - x + 2 ⇒ x(x - 2) - 1(x - 2) ⇒ (x - 1)(x - 2). So, we can say (x - 1) and (x - 2) are the factors of x 3 - ax 2 + b. By factor theorem, A polynomial f(x) has a factor (x - a), if and only if, f(a) = 0. Given, 1st factor ⇒ x - 1 = 0 ⇒ x = 1. Substituting x = 1 in x 3 - ax 2 + b, will give remainder = 0. ⇒ 1 3 - a(1) 2 + b = 0 ⇒ 1 - a + b = 0 ⇒ a = b + 1 .........(Eq. 1) Given, 2nd factor ⇒ x - 2 = 0 ⇒ x = 2. Substituting x = 2 in x 3 - ax 2 + b, will give remainder = 0. ⇒ 2 3 - a(2) 2 + b = 0 ⇒ 8 - 4a + b = 0 ⇒ 4a = b + 8 Substituting value of a from Eq 1 in above equation : ⇒ 4(b + 1) = b + 8 ⇒ 4b + 4 = b + 8 ⇒ 4b - b = 8 - 4 ⇒ 3b = 4 ⇒ b = ⇒ a = b + 1 = . Hence, a = and b = .

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The radii of two concentric circles are 6 cm and 10 cm respectively. Find the length of the chord of the bigger circle which is tangent to smaller circle.

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In the given figure, P(-3, -4) is the mid-point of the line segment AB.
Find the coordinates of points A and B. Also, find the equation of the line passing through the point P and also perpendicular to line-segment AB.

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Mathematics

If x² - 3x + 2 is a factor of x³ - ax² + b, find the values of a and b.

Factorisation

Related Questions

The radii of two concentric circles are 6 cm and 10 cm respectively. Find the length of the chord of the bigger circle which is tangent to smaller circle.

In the given figure, P(-3, -4) is the mid-point of the line segment AB.
Find the coordinates of points A and B. Also, find the equation of the line passing through the point P and also perpendicular to line-segment AB.

Mathematics

If x2 - 3x + 2 is a factor of x3 - ax2 + b, find the values of a and b.

Factorisation

Related Questions

The radii of two concentric circles are 6 cm and 10 cm respectively. Find the length of the chord of the bigger circle which is tangent to smaller circle.

In the given figure, P(-3, -4) is the mid-point of the line segment AB.Find the coordinates of points A and B. Also, find the equation of the line passing through the point P and also perpendicular to line-segment AB.

If x² - 3x + 2 is a factor of x³ - ax² + b, find the values of a and b.

In the given figure, P(-3, -4) is the mid-point of the line segment AB.
Find the coordinates of points A and B. Also, find the equation of the line passing through the point P and also perpendicular to line-segment AB.