1) What is the solution of the quadratic equation 2x2 - 7x + 6 = 0 ?
(A) − 3
2 , 2 (B) 3
2 , 2 (C) -2, 3
2 (D) 2, 2
3
(2) What is the sum of first n natural numbers ?
(A) n n 1
2 (B) n
n
2
2 (C) n n 1
2 (D) n n 2
2
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1.
Answer: The solutions are x=3 2 x=2 Explanation: 2x2−7x+6=0 We can Split the Middle Term of this expression to factorise it and thereby find solutions. In this technique, if we have to factorise an expression like ax2+bx+c, we need to think of 2 numbers such that: N1⋅N2=a⋅c=2⋅6=12 AND N1+N2=b=−7 After trying out a few numbers we get N1=−3 and N2=−4 −3⋅−4=12, and −3+(−4)=−7 2x2−7x+6=0=2x2−4x−3x+6 2x(x−2)−3(x−2)=0 (2x−3)(x−2)=0 Now we equate the factors to zero and obtain solutions. 2x−3=0,x=3 2 x−2=0,x=2
2.Sum of First n Natural Numbers. We prove the formula 1+ 2+ ... + n = n(n+1) / 2, for n a natural number
Answer: The solutions are x=3 2 x=2 Explanation: 2x2−7x+6=0 We can Split the Middle Term of this expression to factorise it and thereby find solutions. In this technique, if we have to factorise an expression like ax2+bx+c, we need to think of 2 numbers such that: N1⋅N2=a⋅c=2⋅6=12 AND N1+N2=b=−7 After trying out a few numbers we get N1=−3 and N2=−4 −3⋅−4=12, and −3+(−4)=−7 2x2−7x+6=0=2x2−4x−3x+6 2x(x−2)−3(x−2)=0 (2x−3)(x−2)=0 Now we equate the factors to zero and obtain solutions. 2x−3=0,x=3 2 x−2=0,x=2
2.Sum of First n Natural Numbers. We prove the formula 1+ 2+ ... + n = n(n+1) / 2, for n a natural number
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