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Complete 10th Class Maths Solution
- NCERT Solutions For Class 10 Maths – Chapter 1 Exercise 1.2 Real Number
- NCERT Solutions For Class 10 Maths – Chapter 1 Exercise 1.3 Real Number
- NCERT Solutions For Class 10 Maths – Chapter 1 Exercise 1.4 Real Number
EXERCISE 2.2
QUE:-1 FIND THE ZEROES OF THE FOLLOWING QUDRATIC POLYNOMIALS AND VERIFY THE RELATIONSHIP BETWEEN THE ZEROES AND THE COEFFICIENTS.
(i) x²-2x-8 (ii) 4s² -4s+ 1 (iii) 6x² -3-7x (iv) 4u² +8u (v) t² -15 (vi) 3x²-x-4
SOL :-
(i) x²-2x-8 =(x-4) (x+2)
the value of x²-2x-8 is zero when x-4 =0 or x+2 =0 i.e.,when x =4 or x= -2
therefore, the zeroes of x²-2x-8 are 4 and -2
sum of zeroes 4-2=2= -(-2)/1=-(COEFFICIENT OF X)/(COEFFICIENT OF X²)
product of zeroes = 4×(-2)=-8=(-8)/1=contant term/coefficient of x²
(ii) 4s² -4s+ 1 =(2s-1)²
the value of 4s² -4s+ 1 is zero when 2s-1 =0 i.e.,when s =1/2
therefore, the zeroes of 4s² -4s+ 1 are 1/2 and 1/2
sum of zeroes 1/2 +1/2 =1= -(-4)/4=-(COEFFICIENT OF S)/(COEFFICIENT OFS²)
product of zeroes = 1/2×1/2=1/4=contant term/coefficient of S²
(iii) 6x² -3-7x =(3x+1) (2x-3)
the value of 6x² -3-7x is zero when 3x+1 =0 or 2x-3 =0 i.e.,when x =-1/3 or x= 3/2
therefore, the zeroes of 6x² -3-7x are -1/3and 3/2
sum of zeroes=-1/3+3/2=7/6= -(-7)/6=-(COEFFICIENT OF X)/(COEFFICIENT OF X²)
product of zeroes = -1/3×3/2=-1/2=(-3)/6=contant term/coefficient of x²
(iv) 4u² +8u =4u² +8u+0
=4u (u+2)
the value of 4u² +8u is zero when 4u =0 or u+2 =0 i.e.,when u =0or u= -2
therefore, the zeroes of 4u² +8u are 0 and -2
sum of zeroes 0+(-2)=-2= -(8)/4=-(COEFFICIENT OF U)/(COEFFICIENT OF U²)
product of zeroes = 0×(-2)=0=(0)/4=contant term/coefficient of u²
(v) t² -15
=t²-0t-15
= (t- root15)(t+root15)
the value of t² -15 is zero when t- root15 =0 or t+root15 =0 i.e.,when t=root15or t= -root15
therefore, the zeroes of t² -15 are root15 and -root15
sum of zeroes root15+(-root15)=0= -(0)/1=-(COEFFICIENT OF T)/(COEFFICIENT OF T²)
product of zeroes = root15×(-root15)=-15=(-15)/1=contant term/coefficient of t²
(vi) 3x²-x-4=(3x-4) (x+1)
the value of 3x²-x-4 is zero when 3x-4 =0 or x+1 =0 i.e.,when x =4/3 or x= -1
therefore, the zeroes of 3x²-x-4 are 4/3 and -1
sum of zeroes 4/3+(-1)=1/3= -(-1)/3=-(COEFFICIENT OF X)/(COEFFICIENT OF X²)
product of zeroes = 4/3×(-1)=-4/3=(-4)/3=contant term/coefficient of x²
QUE:- FIND A QUADRATIC POLYNOMIAL EACH WITH THE GIVEN NUMBERS AS THE SUM AND PRODUCT OF ITS ZEROES RESPECTIVELY.
(i) 1/4,-1 (ii) ROOT 2 , 1/3 (iii) 0, ROOT 5,(iv) 1,1 (v) -1/4,1/4 (vi) 4,1
SOL :-
(i) 1/4,-1
let the polynomial be ax²+bx+c and its zeroes be α and β
α+β =1/4=-b/a
αβ =-1=-4/4=c/b
if a=4, then b=-1,c=-4
therefore ,the quadratic polynomial is 4x²-x-4
(ii) ROOT 2 , 1/3
let the polynomial be ax²+bx+c and its zeroes be α and β
α+β =ROOT 2=3root2/3=-b/a
αβ =1/3=c/b
if a=3, then b=-3root2,c=1
therefore ,the quadratic polynomial is 3x²-3root2x+1 .
(iii) 0, ROOT 5
let the polynomial be ax²+bx+c and its zeroes be α and β
α+β =0=0/1=-b/a
αβ =ROOT 5=c/b
if a=1, then b=0,c=ROOT 5
therefore ,the quadratic polynomial is x²+ROOT 5 .
(iv) 1,1
let the polynomial be ax²+bx+c and its zeroes be α and β
α+β =1=1/1=-b/a
αβ =1=1/1=c/b
if a=1, then b=1,c=1
therefore ,the quadratic polynomial is x²-x+1 .
(v) -1/4,1/4
let the polynomial be ax²+bx+c and its zeroes be α and β
α+β =-1/4=-b/a
αβ =1/4=c/b
if a=4, then b=1,c=1
therefore ,the quadratic polynomial is 4x²+x+1 .
(vi) 4,1
let the polynomial be ax²+bx+c and its zeroes be α and β
α+β =4=-b/a
αβ =1=c/b
if a=1, then b=-4,c=1
therefore ,the quadratic polynomial is x²-4x+1 .
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