GATE 2020 AG – Question 9
General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice
The quadratic $ax^2-bx+c=0$ has equal real roots β. Which relation follows?
- $\beta=b/a$
- $\beta^2=ac$
- $\beta^3=bc/(2a^2)$
- $b^2\ne4ac$
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (C) $\beta^3=bc/(2a^2)$
Explanation
Equal roots give 2β=b/a and β²=c/a. Multiply these relations: β³=bc/(2a²), C. The discriminant is zero, not nonzero, and the root itself is b/(2a).
More Quantitative Aptitude: Algebra, Geometry and Mensuration questions
- GATE 2020 PI Q9 – The graph shows XY varying linearly with Z along a straight line through the origin. Which…
- GATE 2020 ST Q5 – Subtract the sum of the first n odd positive integers from the sum of the first2n positive…
- GATE 2020 ST Q8 – Delhi and Agra are233 km apart. Car P leaves Delhi; Q leaves Agra toward Delhi one hour…
- GATE 2020 ST Q9 – A4×4 matrix has zero diagonal and mij=−mji. How many independent elements fully specify…
- GATE 2021 XH2 Q3 – O is the centre of the circle and M and N lie on it. Right triangle MON has area50 cm².…
- GATE 2021 XH2 Q4 – Here ⊕ means subtraction, ⊗ division, Δ addition and ∇ multiplication. Evaluate Δ2 ⊕3…
All Quantitative Aptitude: Algebra, Geometry and Mensuration questions →