Q. 53.8( 44 Votes )
Let us construct the quadratic equations in one variable from the following statements.
i. Divide 42 into two parts such that one part is equal to the square of the other part.
ii. The product two consecutive positive odd numbers is 143.
iii. The sum of the squares of two consecutive numbers is 313.
Answer :
(i) Let one part be x.
And the other part = x2
Therefore, according to equation
x2 + x = 42
⇒ x2 + x – 42 = 0
(ii) Let the positive odd number be x + 1
The other consecutive positive odd number = (x + 1) + 2 = x + 3
According to question,
(x + 1)(x + 3) = 143
⇒ x2 + 3x + x + 3 = 143
⇒ x2 + 4x + 3-143 = 0
⇒ x2 + 4x -140 = 0
(iii) Let the first number be x.
And the other consecutive number = x + 1
According to question,
x2 + (x + 1)2 = 313
⇒ x2 + x2 + 1 + 2x = 313
⇒ 2x2 + 2x + 1 – 313 = 0
⇒ 2x2 + 2x - 312 = 0
Rate this question :
Linear Equation in one Variable47 mins
Bonus Questions on Solutions of Quadratic Equations31 mins
Get To Know About Quadratic Formula42 mins
Smart Revision | Quadratic Equations53 mins
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Learn to Find Nature of Roots25 mins
Smart Revision | Learn to Find the Nature of Roots34 mins
Nature of Roots of Quadratic Equations51 mins
In each of the following cases, let us justify & write whether the given values are the of the given quadratic equation:
and 4/3
If 
let us calculate the simplified value of
If we subtract 
from 
the value is
Let us write a rationalizing factor of the denominator of 
which is not its conjugate surd.
The highest power of the variable in a quadratic equation is
West Bengal Board - MathematicsLet us rationalizing the denominators of the following surds.
Let us write two mixed quadratic surds of which product is a rational number.
West Bengal Board - MathematicsIf 
let us calculate simplified value of
Let us calculate and write the value of k for which –a will be a root the quadratic equation x2 + 3ax + k = 0.
West Bengal Board - MathematicsLet us rationalizing the denominators of the following surds.
