Let us construct the quadratic equations in one variable from the following statement :
(i) The sum of the squares of two consecutive number is 313
ii) One person bought some kg.sugar at ₹80. if he would get 4 kg more sugar with that money, then the price of 1 kg sugar would be less by ₹1
Answers
Answer:
write quadratic polynomials from the following polynomials by understanding it.
(i) x2-7x+2
(ii) 7x5-x(x+5)+1
(iii) 2x (x+5)+1
(iv) 2x-1
2.Which of the following equations can be written in the form of ax2+bx+c=0, where c, b, c are real numbers and a≠0, let us write it.
3. Let us determine the power of the variable for which the equation x6-x3-2=0 will become a quadratic equation?
4.(i) Let us determine the value of ‘a’ for which the equation (a-2)x2+3x+5=0 will not be a quadratic equation?
4.(ii) If x/4-x = 1/3x, (x≠0, x≠4) be expressed in the form of ax2+bx+c= (a≠0), then let us determine the co-efficient of x.
4.(iii) Let us express the equation 3x2+7x+23 = (x+4) (x+3) +2 in the form of the quadratic equation ax2+bx+c=0 (a≠0)
4.(iv) Let us express the equation (x+2)3 = x(x2-1) in the form of ax2+bx+c=0 (a≠0) and write the co-efficient of x2, x and x0.
5. Let us construct the quadratic equation in one variable from the following statements.
(i) Divide 42 into two part such that one part is equal to the square of the other part.
5.(ii) The product of two consecutive positive odd numbers is 143.
5.(iii) The sum of the squares of two consecutive number is 313.
6. let us construct the quadratic equations in one variable from the following statements.
(i) The length of the diagonal of a rectangular area is 15 m and the length exceeds its breadth by 3 m.
6.(ii) One person bought some kg sugar in ₹80. If he would get 4 kg more sugar with that money, then the price of 1 kg sugar would be less by ₹ 1.
6.(iii) The distance between two stations is 300 km. A train went to second station from first station with uniform velocity. If the velocity of the train is 5km/hour more, then the time taken by the train to reach the second station would be lesser by 2 hours.
6.(iv) A clock seller sold a clock by producing it at ₹ 336. The amount of his profit percentage is as much as the amount with which he bought the clock.
6.(v) If the velocity of the stream is 2 kms/hr, then the time taken by Ratanmajhi to cover 21 kms in down stream and upstream is 10 hours.
6.(vi) The time taken to clean out garden by Majid is 3 hours more than Mahim. Both of them together can complete the work in 2 hours.
6.(vii) The unit digit of a two digit number exceeds its tens’ digit by 6 and the product of two digits is less by 12 from the number.
6.(viii) There is a road of equal width around the outside of a rectangular playground having the length 45 m and breadth 40 m and the area of the road is 450 sqm.
Exercise 1.2
1.In each of the following cases, let us justify & write whether the given values are the root of the given quadratic equation:
2.(i) Let us calculate and write the value of k for which 2/3 will be a root the quadratic equation 7x2+x+1 = 0.
2.(ii) Let us
calculate and write the value of k for which -a will be a root the quadratic equation
x2+3ax+k = 0.
3. If 2/3 and -3 are the two roots of the quadratic equation ax2+7x+b = 0, then let me calculate the values of a and b.
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