What is the NO-SHORTCUT approach for learning great Mathematics?

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Try this beautiful problem from Algebra based on quadratic equation.

Let $d$ and $e$ denote the solutions of $2x^{2}+3x-5=0$. What is the value of $(d-1)(e-1)$?

- \(2\)
- \(0\)
- \(\frac{7}{2}\)

algebra

quadratic equation

Roots

But try the problem first...

Answer: \(0\)

Source

Suggested Reading

AMC-10A (2003) Problem 5

Pre College Mathematics

First hint

To find out the value of \((d-1)(e-1)\),at first we have to find out the value of \(d\) and \(e\).Given that \(d\) and \(e\) are the solutions of the equations $2x^{2}+3x-5=0$ that means \(d\) and \(e\) are the roots of the given equation.so if we find out the values of roots from the given equation then we will get \(d\) and \(e\).Can you find out the roots?

Can you now finish the problem ..........

Second Hint

**To find out the roots :**

The given equation is \(2x^{2}+3x-5=0\) \(\Rightarrow (2x+5)(x-1)=0\) \(\Rightarrow x=1 or \frac{-5}{2}\)

Therefore the values of \(d\) and \(e\) are \(1\) and \(\frac{-5}{2}\) respectively

can you finish the problem........

Final Step

Therefore \((d-1)(e-1)\)=\((1-1)(\frac{-5}{2} -1)\)=\(0\)

- https://www.cheenta.com/ratio-of-lcm-gcf-algebra-amc-8-2013-problem-10/
- https://www.youtube.com/watch?v=V01neV8qmh4

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