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Polynomials

Long Answer Type

431. If α, β are the zeroes of quadratic polynomial 2x² – 3x – 5, form a quadratic polynomial whose zeroes are α² and β².

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432. If α, β are the zeroes of quadratic poly-nomial x² – 3x + 2, form a quadratic polynomial whose roots are –α and –β.

161 Views

433. If α, β are the zeroes of quadratic polynomial x² – 3x – 1, form a quadratic polynomial whose roots are

1 over straight alpha squared comma space 1 over straight beta squared.

122 Views

434. Factorize 2x⁴ + x³ – 14x² – 19x – 6 by x² + 3x + 2 and verify the division algorithm.

163 Views

Short Answer Type

435. Find all the zeroes of the polynomial x³ + 3x² – 2x – 6, if two of its zeroes are –

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1188 Views

436. Find all the zeroes of the polynomial 2a³ + x² – 6x – 3, if two of its zeroes are - $square root of 3 space and space square root of 3.$

Since two zeroes are -

space space space square root of 3 space and space square root of 3

rightwards double arrow

space space space space space left parenthesis x plus square root of 3 right parenthesis space left parenthesis x minus square root of 3 right parenthesis space equals space

x² – 3 is a factor of the given polynomial.
Now, we divide the given polynomial by x²– 3.
Since two zeroes are - . x2 – 3 is a factor of the given pol

Hence, the zeroes of the given polynomial are

space space square root of 3 comma space space minus square root of 3 comma space minus 1 half

230 Views

437. If the polynomial 6x⁴+8x³ + 17x² + 21x + 7 is divided by another polynomial 3x²+ 4x +1, the remainder comes out to be (ax + b), find a and b.

2132 Views

438. If the polynomial x³ + 2x³ + 8x² + 12x + 18 is divided by another polynomial x² + 5, the remainder comes out to be px + q. Find the values of p and q.

211 Views