Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) $\frac{1}{4}$ , $- 1$ (ii) $2, \frac{1}{3}$ (iii) $0, 5$
(iv) $1, 1$ (v) $\frac{- 1}{4}, \frac{1}{4}$ (vi) $4, 1$

Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.(i) 41​, −1 (ii) 2​,31​ (iii) 0,5​(iv) 1,1 (v) 4−1​,41​ (vi) 4,1

Filo · Accepted Answer

(i) 41​, -1Using the quadratic equation formula,x2−(Sum  of  root)x+(Product  of  root)=0Substitute the value in the formula, we getx2−41​x −1=04x2−x−4=0(ii) 2​,31​Using the quadratic equation formula,x2−(Sum  of  root)x+(Product  of  root)=0Substitute the value in the formula, we getx2−2​x+31​=0Multiply by 3 to remove denominator, 3x2−32​x+1=0(iii) 0, 5​Using the quadratic equation formula,x2−(Sum  of  root)x+(Product  of  root)=0Substitute the value in the formula, we getx2−0x+5​=0x2+5​=0(iv) 1, 1Using the quadratic equation formula,x2−(Sum  of  root)x+(Product  of  root)=0Substitute the value in the formula, we getx2−1x+1=0x2−x+1=0(v) 4−1​,41​Using the quadratic equation formula,x2−(Sum  of  root)x+(Product  of  root)=0Substitute the value in the formula, we getx2−4−1​x+41​=0Multiply by 44x2+x+1=0(vi) 4, 1Using the quadratic equation formula,x2−(Sum  of  root)x+(Product  of  root)=0Substitute the value in the formula, we getx2−4x+1=0

Question Text	Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) $\frac{1}{4}$ , $- 1$ (ii) $2, \frac{1}{3}$ (iii) $0, 5$ (iv) $1, 1$ (v) $\frac{- 1}{4}, \frac{1}{4}$ (vi) $4, 1$
Answer Type	Text solution:1
Upvotes	150

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) $\frac{1}{4}$ , $- 1$ (ii) $2, \frac{1}{3}$ (iii) $0, 5$
(iv) $1, 1$ (v) $\frac{- 1}{4}, \frac{1}{4}$ (vi) $4, 1$

Text solutionVerified

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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.(i) 41​, −1 (ii) 2​,31​ (iii) 0,5​(iv) 1,1 (v) 4−1​,41​ (vi) 4,1

Text solutionVerified

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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) $\frac{1}{4}$ , $- 1$ (ii) $2, \frac{1}{3}$ (iii) $0, 5$
(iv) $1, 1$ (v) $\frac{- 1}{4}, \frac{1}{4}$ (vi) $4, 1$