Polynomials

Mathematics For Class 10
Polynomials

Q 1   If the sum of the squares of the roots of the equation x² + 2x – p = 0 is 8, find the value of p

Q 2   If one root of the equation 6x² + 13x+ m = 0 is reciprocal of the other, find the value of m. 

Q 3 If f(x) = ax³ + bx² + cx + d, a ≠ 0, then what will be the sum of zeros?                              

Q 4 If the sum of the zeroes of the polynomial f(x) = 2x³ - 3kx² + 4x - 5 is 6, then find the value of k. 

Q 5 Find a quadratic polynomial, if the sum and the product of the zeroes are 4 and 4 respectively.

Q 6 The product of two zeroes of the polynomial f(x) = 2x³ + 6x² -4x + 9 is 3, then find its third zero.      

Q 7 If (x + 2)(2x - 1)(3x - 2) = 0, find the zeroes of the polynomial

Q 8 Find a quadratic polynomial, the sum and product of its zeroes are 1 and –6 respectively. 

 Q 9 Find a quadratic equation, whose roots are(1+√5) and (1-√5)  

Q 10 Find a quadratic polynomial, the sum and product of its zeroes are 8 and 15 respectively.
Q 11 Find a quadratic polynomial, the sum and product of whose zeroes are -7 and 7 respectively.
Q 12 Find a quadratic polynomial, the sum and product of whose zeroes are -5 and 4 respectively.           

Q 13 Find a quadratic polynomial, the sum and product of whose zeroes are –3 and 2 respectively.    
Q 14 Find the quadratic polynomials, the sum and product of whose zeroes are 4 and 1 respectively.  
Q 15 If α and β  are the root of  the equation ax² + bx + c= 0  Find the value of 1/α     + 1/β

Q 16 If α and β are the roots of the equation 25x² - 10x + 1= 0, find the value of α² + β².  

Q 17 If the zeroes of the polynomial f(x) = x³ - 3x + x + 1 are  a – b, a and a + b find a, b.
Q 18 If αand β are the zeroes of the polynomials f(x) = x² - px + q, find the value of α²+β².
Q 19 If αand β are the zeroes of a quadratic polynomial such that α+ β = 24 and α- β = 8, then find the quadratic polynomial. 

Q 20  Find a quadratic polynomial , the sum of whose Zero is  -1 and sum of their reciprocal is  1/6 

Q 21 Write a quadratic polynomial , the sum of whose roots  is  2√3and sum of their reciprocal is  2.

Q 22 If α and β are the root ofs of a ax² -  b x + c= 0 , what is the value of √ α/β     + √β/α

  

Q 23 If α and β are the zeroes of polynomial 9x² - 3x - 2, evaluate α^-1 + β^-1. 

Q 24 A quadratic polynomial 2x² - mx + n has α and β as its two zeroes. Evaluate α² + (β)2. 

Q 25 Find a cubic polynomial with the sum, sum of the products of its zeroes taken two at a time, and the product of its zeroes as 2, - 7 and –14 respectively. 

Q 26 If α, β are the roots of the equation 3x² - 4x + 1 = 0, find the value of  α³ + β³.

Q 27 If the zeroes of the polynomial f(x)  = x³  - 3x² + x + 1 are a – b, a and a + b, find the values of a and b.
Q 28 If α and β are the zeroes of the quadratic polynomial f(x) = ax² + bx + c, then evaluate α²β + αβ². 

 Q 29If α and β are the zeroes of the polynomial p(x) = x² - 16x + 63, then find the value of α⁴β³ + α³β⁴.

Q 30 If the sum of the squares of the zeroes of a quadratic polynomial x^­­­2 –18x + p is 180, find the value of p.