हिंदी

If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

Advertisements
Advertisements

प्रश्न

If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is True.

Explanation:

Because in this case discriminant is always negative.

For example, in ax2+ bx + c = 0, as b = 0

And a and c have same sign then ac > 0

⇒ Discriminant = b2 – 4ac = – 4 a c < 0

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Quadatric Euation - Exercise 4.2 [पृष्ठ ३८]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 10
अध्याय 4 Quadatric Euation
Exercise 4.2 | Q 2.(vi) | पृष्ठ ३८

संबंधित प्रश्न

 

Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3

 

Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.


Find the values of k for which the roots are real and equal in each of the following equation:

x2 - 2(5 + 2k)x + 3(7 + 10k) = 0


If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x2 + 5(p + q) x− 2(p − q) = 0 are real and unequal.


Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?


`(2)/x^2 - (5)/x + 2` = 0


`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0


`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0


Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0


Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0


Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.


If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0.


If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:


If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 – q2)x2 – (q2 – r2)x + (r2 – p2) = 0 are:


Which of the following equations has the sum of its roots as 3?


(x2 + 1)2 – x2 = 0 has ______.


Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.


Find whether the following equation have real roots. If real roots exist, find them.

`x^2 + 5sqrt(5)x - 70 = 0`


The roots of quadratic equation x2 – 1 = 0 are ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×