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Class 10 Class 12

Polynomials

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

What real number should be subtracted from the polynomial 3x² + 10x²– 14x + 9, so that the polynomial 3x– 2 divides it exactly ?

Let p(x) = $space space 3 straight x squared plus 10 straight x squared minus 14 straight x plus 9$
$straight q left parenthesis straight x right parenthesis space equals space 3 straight x minus 2 comma space$ dividing p(x) by q(x), we get
Let p(x) = dividing p(x) by q(x), we getAns. 5.
Ans. 5.

134 Views

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

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Since two zeroes are -

square root of 2 space and space square root of 2

= x² – 2 is a factor of the given polynomial.
Now, we divide the given polynomial by x²–2.
Since two zeroes are - = x2 – 2 is a factor of the given polynom

Hence, the zeroes of the given polynomial are

space space square root of 2. space square root of 2 space Ans. space

1188 Views

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.