Quadratic Equation (One Variable)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

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Question No: #61

Find the equation whose roots are square of the roots of `2x^2+3x+1=0`

Question No: #62

If the roots of the equation `x^2-2x+2=0` are `\alpha` and `\beta`, find the equation whose roots are `(\alpha+2)` and `(\beta+2)`.

Question No: #63

If `a+b+c=0`, then show that one of the roots of the equation `ax^2+bx+c=0` is `1`.
Alternative question:
If `a, b, c` are rational numbers and `a+b+c=0`, then determine the nature of the roots of the quadratic equation `ax^2+bx+c=0` (`a \ne 0`).
Ans: Real and unequal (বাস্তব ও অসমান)
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Question No: #64

If the roots of the equation `ax^2+bx+c=0` are `\alpha` and `\beta`, then find the value of `(\frac{a\alpha^2}{b\alpha+c}-\frac{a\beta^2}{b\beta+c})`.
Ans: `0`
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Question No: #65

A rectangular field has an area of ​​2000 square meters and perimeter of 180 meters. Find the length and width of the rectangular area.

Question No: #66

The units digit of a two-digit number is 6 more than the tens digit and product of the two digits is 12 less than the number. What could be the units digit of the number?
Ans: 8, 9
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Question No: #67

The tens digit of a two-digited number is 4 less than units digit. If the product of these digits is subtracted from the number, then this subtraction is equal to square of the difference of these two digits. Determine the number.
Ans: 37, 48
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Question No: #68

If the product of two consecutive positive odd numbers is 143, form the equation and find the two numbers using Sridhar Acharya's formula.
Ans: 11, 13
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Question No: #69

If the product of two consecutive even positive numbers is 168, then find the two numbers.
Ans: 12, 14
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Question No: #70

The sum of the squares of two consecutive odd positive integers is 650. Find the numbers.
Ans: 17, 19
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