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Find the value of a, b, c in the following quadratic equation : 2x2 ‒ x ‒ 3 = 0
Concept: Quadratic Equations
Write the quadratic equation whose roots are ‒2 and ‒3.
Concept: Quadratic Equations
Verify whether 1 is the root of the quadratic equation : `x^2+3x-4=0`
Concept: Quadratic Equations
If one root of the quadratic equation kx2 – 7x + 12 = 0 is 3, then find the value of k.
Concept: Quadratic Equations
If α + β = 5 and α3 +β3 = 35, find the quadratic equation whose roots are α and β.
Concept: Quadratic Equations
(x + 5)(x - 2) = 0, find the roots of this quadratic equation
Concept: Quadratic Equations
Write the following quadratic equation in a standard form: 3x2 =10x + 7.
Concept: Quadratic Equations
If 12x +13y =29 and 13x +12y=21, find x + y.
Concept: Linear Equation in Two Variables
The product of four consecutive natural numbers, which are multiples of fives, is Rs. 15,000. Find those natural numbers.
Concept: Linear Equation in Two Variables
The time taken by a person to cover 150 km was 2 1/2 hours more than the time taken in the return journey. If he returned at a speed of 10 km/hour more than the speed while going, find the speed per hour in each direction.
Concept: Quadratic Equations
Find the values of a, b, c for the quadratic equation 2x2 = x + 3 by comparing with standard form ax2 + bx + c = 0.
Concept: Quadratic Equations
Find the value of discriminant (Δ) for the quadratic equation: `x^2+7x+6=0`
Concept: Quadratic Equations
Find the value of k for which the given simultaneous equations have infinitely many solutions:
kx + 4y = 10;
3x + 2y = 5.
Concept: Linear Equation in Two Variables
State whether the given equation is quadratic or not. Give reason.
`5/4m^2 - 7 = 0`
Concept: Quadratic Equations
Write any one solution of equation x + 2y = 7.
Concept: Linear Equation in Two Variables
Find the value of x- y if 4x + 3y = 25, 3x + 4y = 24
Concept: Linear Equation in Two Variables
Solve the following quadratic equation by using formula method :
2x2 - 3x = 2
Concept: Quadratic Equations
A boat takes 10 hours to travel 30 km upstream and 44 km downstream, but it takes 13 hours to travel 40 km upstream and 55 km downstream. Find the speed of the boat in still water and the speed of the stream.
Concept: Linear Equation in Two Variables
Complete the following activity to solve the simultaneous equations.
5x + 3y = 9 -----(I)
2x + 3y = 12 ----- (II)
Concept: Linear Equation in Two Variables
Solve the following simultaneous equation.
3a + 5b = 26; a + 5b = 22
Concept: Linear Equation in Two Variables