Find It Without the Zeroes
If α and β are the zeroes of 2x² − 7x + 4, find α/β + β/α without finding the zeroes.
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Class 10 Maths HOTS questions
HOTS means Higher Order Thinking Skills. These questions cannot be done by putting numbers into one formula. You have to choose a route first. Here are three new ones to solve yourself.
Three HOTS questions to try
From the Sum Back to the Terms
The sum of the first n terms of an AP is 2n² + 7n. Which term of the AP is 101?
Try it step by stepEqual Roots, Two Values of k
Find the values of k for which (k + 2)x² − 2kx + 1 = 0 has equal roots, then find that root.
Try it step by stepEach question is split into small steps. If you get stuck, the hints ask you a question that points the way. They never just show you the answer. Every question was written for Young Math Brains and checked twice.
How to think through a HOTS question
- Before calculating, ask what the question lets you skip. You can often find α/β + β/α without finding α and β.
- Rewrite what you are asked for in terms of what you are given, such as α + β and αβ for zeroes, or S₁ and S₂ for an AP.
- A sum formula Sₙ hides the whole AP. The first term is S₁ and the second term is S₂ − S₁.
- When an unknown such as k sits inside a coefficient, turn the condition (equal roots, a zero is three times the other) into an equation in k.
- Check your values at the end. A value of k that makes the x² coefficient zero no longer gives a quadratic.
Want questions like these for every chapter?
Young Math Brains has lessons, practice and board-style tests for all 14 chapters of CBSE Class 10 Maths, and every answer is checked. Start free with Pair of Linear Equations. No card needed.