Latest Posts

State whether the following quadratic equations have two distinct real roots. Justify your answer. i) x² – 3x + 4 = 0 ii) 2x² + x – 1 = 0 iii) 2x² – 6x + 9/2 = 0 iv) 3x² – 4x + 1 = 0 v) (x + 4)² – 8x = 0 vi) (x – √2)² – 2(x + 1) = 0 vii) √2 x² -(3/√2)x + 1/√2 = 0 viii) x (1 – x) – 2 = 0 ix) (x – 1) (x + 2) + 2 = 0 x) (x + 1) (x – 2) + x = 0

Solution: (i) x2 – 3x + 4 = 0 The given quadratic equation x2 – 3x + 4 = 0 has no real... View Article

Which of the following equations has the sum of its roots as 3? (A) 2x² – 3x + 6 = 0 (B) -x² + 3x – 3 = 0 (C) √2x² – 3/√2x+1=0 (D) 3x² – 3x + 3 = 0

Answer The correct answer is (B) –x2 + 3x – 3 = 0 The sum of the roots of a quadratic... View Article

If ½ is a root of the equation x² + kx – 5/4 = 0, then the value of k is (A) 2 (B) – 2 (C) ¼ (D) ½

Answer The correct answer is (A) 2 Solution If ½ is a root of the equation x2 + kx – 5/4 =... View Article

Which of the following equations has 2 as a root? (A) x² – 4x + 5 = 0 (B) x² + 3x – 12 = 0 (C) 2x² – 7x + 6 = 0 (D) 3x² – 6x – 2 = 0

Answer The correct answer is (C) 2x2 – 7x + 6 = 0 Solution If 2 is a root then substituting the... View Article

Which of the following is not a quadratic equation? (A) 2(x – 1) = 4x² – 2x + 1 (B) 2x – x² = x² + 5 (C) (√2x + √3)² + x² = 3x² − 5x (D) (x² + 2x)² = x⁴ + 3 + 4x³

Answer The correct answer is (D) (x2 + 2x)2 = x4 + 3 + 4x3 Solution We know that a quadratic equation is represented... View Article

Which of the following is a quadratic equation? (A) x² + 2x + 1 = (4 – x)² + 3 (B) -2x² = (5 – x)(2x-(2/5)) (C) (k + 1) x² + (3/2) x = 7, where k = -1 (D) x³ – x² = (x – 1)3

Answer The correct answer is (D) x3 – x2 = (x – 1)3 Solution We know that the standard form of a quadratic equation is... View Article

Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus.

Given Distance travelled by Ankita to her home partly by rickshaw and partly by bus= 14km She takes half an... View Article

Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3 2x – 3y = 2 x + 2y = 8

3x – y = 2 …(1) 2x -3y = 2 …(2) x + 2y = 8 …(3) Let the equations... View Article

The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box.

Given The cost of 4 pens and 4 pencil boxes = Rs 100 Three times the cost of a pen... View Article

Draw the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0. Also find the area of the quadrilateral formed by the lines and the x-axis.

Solution Given equation of lines x = 3, x = 5 and 2x-y-4 = 0. Table for line 2x –... View Article

Determine, graphically, the vertices of the triangle formed by the lines y = x, 3y = x, x + y = 8

Solution Given linear equations are y = x …(i) 3y = x …(ii) and x + y = 8 …(iii)... View Article

Graphically, solve the following pair of equations: 2x + y = 6 2x – y + 2 = 0 Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Solution Given equations are 2x + y = 6 2x – y + 2 = 0 Table for equation 2x... View Article

Two straight paths are represented by the equations x – 3y = 2 and -2x + 6y = 5.Check whether the paths cross each other or not.

Given Given pair of linear equations is x – 3y – 2 = 0 …(i) -2x + 6y – 5... View Article

Find the value(s) of p and q in the following pair of equations: 2x + 3y = 7 and 2px + py = 28 – qy, if the pair of equations have infinitely many solutions.

Given Given pair of linear equations is 2x + 3y = 7 2px + py = 28 – qy or... View Article

Find the value(s) of p in the following pair of equations: 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.

Given Given pair of linear equations is 2x + 3y – 5 = 0 px – 6y – 8 =... View Article

Find the value(s) of p in the following pair of equations: – 3x + 5y = 7 and 2px – 3y = 1, if the lines represented by these equations are intersecting at a unique point.

Given Given pair of linear equations is – 3x + 5y = 7 2px – 3y = 1 Find out... View Article

Find the value(s) of p in the following pair of equations: – x + py = 1 and px – y = 1, if the pair of equations has no solution.

Given Given pair of linear equations is – x + py = 1 …(i) px – y – 1 =... View Article

«
1
…
1,469
1,470
1,471
1,472
1,473
…
5,472
»