Quadratic Equations (IMO- Mathematics Olympiad Class 10): Questions 66 - 69 of 80

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Question number: 66

» Quadratic Equations

MCQ▾

Question

Sum of two numbers x and y is 8 and the absolute value of their difference is 10 the equation with these numbers as roots is ________

Choices

Choice (4) Response
a.

x28x+9=0

b.

x28x+9=0

c.

x28x9=0

d.

x2+8x9=0

Question number: 67

» Quadratic Equations

MCQ▾

Question

If the roots of equation a1x2+a2x+a3=0 are in the ratio r1:r2 , then

Choices

Choice (4) Response
a.

r1.r2.a12=(r1+r2)a32

b.

r1.r2.a22=(r1+r2)2a1.a3

c.

r1.r2.a2=(r1+a2)2a1.a2

d.

r1.r2.a12=(r1+r2)2a3.a2

Question number: 68

» Quadratic Equations

MCQ▾

Question

In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 15 bangles with him. If he wanted to increase the size of square by one unit each side of the square he found that 16 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was ________

Choices

Choice (4) Response
a.

310

b.

240

c.

290

d.

260

Question number: 69

» Quadratic Equations

MCQ▾

Question

In the Maths Olympiad of 2030 at X Planet, two representatives from the Sejm’s side, while solving a quadratic equation, committed the following mistakes:

  1. One of them made a mistake in the constant term and got the roots as -14 and 6.
  2. Another one committed an error in the coefficient of x and he got the roots as 3 and -6

But in the meantime, they realized that they are wrong and they managed to get it right jointly. Find the quadratic equation.

Choices

Choice (4) Response
a.

x2+8x+18=0

b.

x28x+18=0

c.

x2+8x18=0

d.

x28x18=0

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