Question

*SUBJECT:MATHEMATICS*
*MARKS:20*
*A.Fill in the blanks 1×4=4*
1.The zeroes of the polynomial t²-15 are ___
2.The sum and product of zeroes of the polynomial are 4 and 5 then the quadratic polynomial is___-
3.If b²-4ac>0,then the quadratic equation has ___roots.
4.The general form of the quadratic equation is___
*B.Answer the following 2×5=10*
1.Find the zeroes of the quadratic polynomial x²-2x-8 and verify the relationship between the zeroes and the coefficients.
2.Divide the polynomial p(x)=x³-3x²+5x-3 by the polynomial g(x)=x²-2 and find the quotient and remainder.
3.Find two numbers whose sum is 27 and product is 182
4.Find the roots of 2x²-7x+3=0 by applying quadratic formula.
5.Find the nature of the roots of the quadratic equation 2x²-3x+5=0.
*C.Answer the following 3×2=6*
1.On dividing p(x)=x³-3x²+x+2 by a polynomial g(x),the quotient and remainder were x-2 and -2x+4 respectively.Find g(x).
2.A train travels 360km at a uniform speed.If the speed had been 5km/ h more,it would have taken 1hr less for the same journey .Find the speed of the train.

Answer 1

I hope it's help you

Plz mark my answer as a brainliest answer

Answer 2

Answer:

The roots of quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation. For example, the roots of the quadratic equation x2 - 7x + 10 = 0 are x = 2 and x = 5 because they satisfy the equation. i.e.,

when x = 2, 22 - 7(2) + 10 = 4 - 14 + 10 = 0.

when x = 5, 52 - 7(5) + 10 = 25 - 35 + 10 = 0.

But how to find the roots of a general quadratic equation ax2 + bx + c = 0? Let us try to solve it for x by completing the square.

ax2 + bx = - c

Dividing both sides by 'a',

x2 + (b/a) x = - c/a

Here, the coefficient of x is b/a. Half of it is b/(2a). Its square is b2/4a2. Adding b2/4a2 on both sides,

x2 + (b/a) x + b2/4a2 = (b2/4a2) - (c/a)

[ x + (b/2a) ]2 = (b2 - 4ac) / 4a2 (using (a + b)² formula)

Taking square root on both sides,

x + (b/2a) = ±√ (b² - 4ac) / 4a²

x + (b/2a) = ±√ (b² - 4ac) / 2a

Subtracting b/2a from both sides,

x = (-b/2a) ±√ (b² - 4ac) / 2a (or)

x = (-b ± √ (b² - 4ac) )/2a

This is known as the quadratic formula and it can be used to find any type of roots of a quadratic equation.