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.
2x2 + 5x2 − 7
Divide 24a3b3 by −8ab.
Divide 72xyz2 by −9xz.
Divide −72a4b5c8 by −9a2b2c3.
Divide m3 − 14m2 + 37m − 26 by m2 − 12m +13.
Divide 30x4 + 11x3 − 82x2 − 12x + 48 by 3x2 + 2x − 4 and find the quotient and remainder.
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 6y5 − 28y3 + 3y2 + 30y − 9 | 2y2 − 6 |
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 34x − 22x3 − 12x4 − 10x2 − 75 | 3x + 7 |
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
x4 − x3 + 5x, x − 1
Find whether the first polynomial is a factor of the second.
4x2 − 5, 4x4 + 7x2 + 15
