Advertisements
Advertisements
प्रश्न
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
Advertisements
उत्तर
\[\text{We have to find the value of a if} (x + 2) \text{is a factor of} (4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a) . \]
\[\text{Substituting}\ x = - 2\ \text{in}\ 4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a, \text{we get:} \]
\[4( - 2 )^4 + 2( - 2 )^3 - 3( - 2 )^2 + 8( - 2) + 5a = 0\]
\[or, 64 - 16 - 12 - 16 + 5a = 0\]
\[or, 5a = - 20\]
\[or, a = - 4\]
\[ \therefore If (x + 2) \text{is a factor of}\ (4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a), a = - 4 . \]
APPEARS IN
संबंधित प्रश्न
Write the degree of each of the following polynomials.
Simplify:\[\frac{16 m^3 y^2}{4 m^2 y}\]
Divide −4a3 + 4a2 + a by 2a.
Divide 2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1.
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 14x2 + 13x − 15 | 7x − 4 |
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
5y3 − 6y2 + 6y − 1, 5y − 1
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
y4 + y2, y2 − 2
Find whether the first polynomial is a factor of the second.
4y + 1, 8y2 − 2y + 1
Divide:
x2 − 5x + 6 by x − 3
Divide 27y3 by 3y
