MEDIUM
10th ICSE
IMPORTANT
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If p, q, r & s are real numbers such that pr=2 (q + s ), then show that at least one of the equations x2+px+q=0 and x2+rx+s=0
has real roots.

Important Questions on Quadratic Equations in One Variable

HARD
10th ICSE
IMPORTANT
All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 12
Prove that both the roots of the equation  (x-a)(x-b)+(x -b)(x -c)+(x -c)(x -a)=0 are real but they are equal only which a=b=c.
MEDIUM
10th ICSE
IMPORTANT
All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 1
The sum of the squares of two consecutive natural numbers is 481. Find the sum of two numbers.
MEDIUM
10th ICSE
IMPORTANT
All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 2
The sum of the squares of two consecutive odd positive integers is 290. Find them.
MEDIUM
10th ICSE
IMPORTANT
All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 3
Divide 25 into two parts, such that twice the square of the larger part exceeds thrice the square of the smaller part by  29.
HARD
10th ICSE
IMPORTANT
All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 4
The sum of two numbers is 18. If the sum of their reciprocals is 14, if the numbers are k, 2k then find the value of k.
HARD
10th ICSE
IMPORTANT
All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 5
A two-digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
HARD
10th ICSE
IMPORTANT
All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 6
A two-digit number contains the smaller of two digits in the unit's place. The product of the digits is 24 and the difference between the digits is 5. Find the number.
HARD
10th ICSE
IMPORTANT
All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 7
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by 114 Find the fraction.