If \(\alpha, \beta\) are roots of the equation 2x²-6x+a=0 and \(2\alpha+5\beta=12\) find the value of a.

5

(a)

Solve for x: \(x^2+5x-(a^2+a-6)=0\)

5

(a)

If twice the area of a smaller square is subtracted from the area of the larger square.the result is \(14cm^{ 2 }\) However, if twice the area of the larger square is added to three times the area of the smaller square. the result is \(203cm^{ 2 }\) .Find the sides of the two square.

5

(a)

In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in maths and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately.

5

(a)

In a flight of 2800km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100km/h and time increased by 30 minutes. Find the original duration of the flight.

5

(a)

Solve for x \({x-2\over x-3}+{x-4\over x-5}={10\over 3}, x\ne3,5\)

5

(a)

The perimeter of right-angled triangle is five times the length of its shortest side. The numerical value of the area of the triangle is 15 times the numerical value of the length of the shortest side. Find the lengths of the three sides of the triangle.

5

(a)

One side of a rectangle exceeds its other side by 2cm.If its area is 195 \(cm^{2}\). determine the sides of the rectangle.

5

(a)

The sum of squares of two consecutive even numbers is 340. Find the numbers.

5

(a)

If the equation \((1+m^{ 2 })(x^{ 2 }+2mcx+(c^{ 2 }-a^{ 2 }(1+m^{ 2 })\) has equal roots prove that  c²=a²(1+m²)

5

(a)